What is the process for remarried couples to convert to Catholicism?

In Catholic church you vow to never leave your wife/husband until death. There's no "fix". The only "fix" is to reunite or live apart, but without any new wife/husband. Jesus said exactly that you cannot do such a thing and nothing can change it (thank God).

Since reunion seems impossible, we have to look at the other option. "Suggesting to live like a brother and sister isn't going to work unless they stop living in the same household". In my opinion this is not true. It's about your soul and mind being pure, not living next to each other. It's hard, very hard, but not impossible.

I have friends that were in similar situation (but they were living without marriage). They stopped to have sex, but still lived in the same house (economical reasons). They waited for marriage and succeeded. If you're divorced, problem is not going to solve itself, but that's the consequence of the vow (i.e. your own actions).

You want to be aligned with the Church, you have to be aligned with your vows.

There's a beautiful book by Karol Wojtyla (before he became Pope John Paul II) titled "Milosc i odpowiedzialnosc" (eng. "Love and responsibility"). A little hard to read, but very, very deep. I suggest reading it fully.

Update: Related to the topic is "Familiaris consortio" by John Paul II. It's from 1981 but still accurate and inline with "Amoris Laetitia" (not surprising, is it?)

The process is called convalidation

The diocese of Detroit has a primer on this, which you can read here, but the basics remain the same.

1. The presumption of any marriage is that it is valid unless challenged. (Code of Canon Law).

2. Catholics are obliged to, when they get married, take the effort to ensure that the marriage is sacramental. (Code of Canon Law)

3. Each case has it's own details and nuances. That is a critical point to understand: the pastor, and in some cases the diocese, investigates a marriage that is claimed to not be sacramental and will uncover what defects, if any, are present (Code of Canon Law).

   In some cases a decree of nullity of a previous marriage is first needed, and in other cases (as with a friend of mine who was Catholic, and his wife was Catholic, but they had a civil marriage) a course of instruction and formation is called for (in his and her case, taking the RCIA class through to completion) and then having their marriage convalidated.

4. There are a lot of points in between.

Insofar as "theologians" go: the Catholic Church holds that the man and woman confer the sacrament upon each other (Catechism of the Catholic Church)¹ and the clergy is present (as well as two witnesses) for a variety of reasons - one of which is so that the Church can attest to the truth of the sacrament having been conferred.

About your "hypothetical" case:

This is a situation: A non-practicing Catholic couple "divorces" and re-marry by state.

I presume they get re-married to other people?

They end up having families, let's say with 3 or more kids with another husband/wife. According to the Catholic teaching, they live in adultery.

Strictly speaking, yes, unless a decree of nullity is arrived at with a favoarble finding.

Now, they start to be interested in spiritual life and undergo what we call a conversion. But they are stuck because they can't just split and leave their kids or whatever dependencies they have.

The simple answer is (even though it is not simple to do):

Convince their spouse to become Catholic. Apply for a decree of nullity. Get the new marriage convalidated. It only takes (from months to years) to go through this.

I know the ideal would be to get an annulment and solve this problem. But let's say they aren't entitled to an annulment.

Entitlement isn't the issue. Each case is investigated for its own particulars. Nobody is entitled to a decree of nullity; such a decree is the finding of a tribunal. The answer can be yes or it can be no. From your stated case, I am not convinced that the two couples have attempted to get decrees of nullity. There may indeed have been a defect that could show that the first marriage was non sacramental. You can't know that until you bother to go through the process.

My question is what does the church offer to such couples as a solution?

I presume that you mean the two new couples? You do not specify that all four people are Catholic.

Suggesting to live like a brother and sister isn't going to work unless they stop living in the same household but that might not be ideal for kids (I guess) or it can still cause a scandal.

For some couples it may work, for others it will not. I've seen both cases ... the outcome varies.

Is splitting couples really the only way to go if they want to live a sacramental life? I know this happened to St. Augustine but his situation wasn't that complicated. Do we have other examples from the past where families needed to separate in order to return back to living in the state of grace?

There is no need to split up the couple, and for sure In My Experience the Church will not promote splitting up the family.

This one hits close to home.

I know a couple (I worked with the husband for seven years) who are still married, in this exact situation, and they come to our church regularly. The two adults do not receive communion, but in all other ways are active members of our parish and are raising their kids to be Catholic. That is a solution. I have encouraged him to pursue convalidation but between the two of them they have not yet chosen that path for their own reasons.

I challenge the frame of this question: this isn't a matter of what theologians write about, this is a matter of sacramental administration under the Code of Canon Law.

How do I know this?

I spent about 6 years in the RCIA ministry and part of that time was spent in helping people through the convalidation process, and the often difficult process of determining whether or not a decree of nullity for a previous marraige was needed. Each case was addressed on its own merits.

¹ Man and woman confer on each other ...

{CCC} II. THE CELEBRATION OF MARRIAGE

1621 In the Latin Rite the celebration of marriage between two Catholic faithful normally takes place during Holy Mass, because of the connection of all the sacraments with the Paschal mystery of Christ. In the Eucharist the memorial of the New Covenant is realized, the New Covenant in which Christ has united himself for ever to the Church, his beloved bride for whom he gave himself up. It is therefore fitting that the spouses should seal their consent to give themselves to each other through the offering of their own lives by uniting it to the offering of Christ for his Church made present in the Eucharistic sacrifice, and by receiving the Eucharist so that, communicating in the same Body and the same Blood of Christ, they may form but "one body" in Christ.

1622 "Inasmuch as it is a sacramental action of sanctification, the liturgical celebration of marriage . . . must be, per se, valid, worthy, and fruitful." It is therefore appropriate for the bride and groom to prepare themselves for the celebration of their marriage by receiving the sacrament of penance.

1623 According to Latin tradition, the spouses as ministers of Christ's grace mutually confer upon each other the sacrament of Matrimony by expressing their consent before the Church. In the tradition of the Eastern Churches, the priests (bishops or presbyters) are witnesses to the mutual consent given by the spouses, but for the validity of the sacrament their blessing is also necessary.

1624 The various liturgies abound in prayers of blessing and epiclesis asking God's grace and blessing on the new couple, especially the bride. In the epiclesis of this sacrament the spouses receive the Holy Spirit as the communion of love of Christ and the Church. The Holy Spirit is the seal of their covenant, the ever available source of their love and the strength to renew their fidelity.

G.K. Chesterton discusses the logical absurdity of pretending to "cancel" a life long vow with a piece of paper from a government in "The Superstition of Divorce". I highly recommend reading or listening to (free on Librivox) this short book.

Disclaimer, I am not Catholic, but try to study their positions seriously. I think a friendly outside perspective may be helpful.

Catholics focus on verifiable objective facts. The couple did make vows as nominal Catholics according to the premises of the question. This can be verified from Church records, signed and witnessed. Protestants focus on subjective realities. Possibly, the individuals were just following family tradition getting married in a Catholic Church, and did not comprehend the seriousness of their vow. The Catholic annulment process attempts to address the situation of making vows in ignorance or under compulsion (forced marriage) or false pretences.

If the the original vows were real, then both parties have been living in adultery, and had multiple kids in adultery. The kids are going to be scarred. The Law of Moses said: "No one of illegitimate (adulterous) birth shall enter the assembly of the LORD unto the 10th generation."

Nevertheless, Children of "putative marriages" (Canon 1061.3 An invalid marriage is said to be putative if it has been celebrated in good faith by at least one party. It ceases to be such when both parties become certain of its nullity.) are considered legitimate by the Catholic Church.

There is no way to unscramble this egg. The Catholic prescription of "living as brother and sister" with the adulterous partners is as good as anything a Protestant denomination might suggest. The Catholic Catechism paragraph 1649 and 1650 ends with:

"Reconciliation through the sacrament of Penance can be granted only to those who have repented for having violated the sign of the covenant and of fidelity to Christ, and who are committed to living in complete continence."

Toward Christians who live in this situation, and who often keep the faith and desire to bring up their children in a Christian manner, priests and the whole community must manifest an attentive solicitude, so that they do not consider themselves separated from the Church, in whose life they can and must participate as baptized persons: They should be encouraged to listen to the Word of God, to attend the Sacrifice of the Mass, to persevere in prayer, to contribute to works of charity and to community efforts for justice, to bring up their children in the Christian faith, to cultivate the spirit and practice of penance and thus implore, day by day, God's grace.

If the original vows were made in ignorance by both parties, then we have two (nominally Catholic) pagan families, at least two members of which now seek to obey Christ and rejoin the Catholic Church. In this case, the original marriage was effectively pagan fornication. This statement does not dismiss the Catholic ceremony - the couple disrespected it while making serious vows they did not mean. In this case, the way forward is clear - stay with the current partners. If the Catholic church cannot annul the vows made in ignorance (due to their unarguable objective reality), then the new marriages cannot be validated with (real this time) vows by the Church, and "living as brother and sister" is again the only option to avoid fornication in the eyes of the Church.

Since the first answer got voted down, I'm sure this one will too. Broken eggs make a big mess. GOD HATES DIVORCE. Malachi 2:13-16

Not mentioned in the question is whether the new partners are also Believers seeking to obey Christ. Are they also Catholic? Or something else?

Now, because you are seeking to Obey Christ, it is up to Christ to make something beautiful out of this screwed up mess. You don't have to understand the whole picture, or know the ultimate outcome. Just do what is clear, and trust God to work all things together for good.

Addendum from comments: Canon law site: http://www.catholicdoors.com/misc/marriage/canonlaw.htm This confirms that the first marriage is the only valid one - but doesn't say what to do about this mess. If there were no children, the clear course would be to separate from the adulterous partners.

It also has a web form to ask questions of a presumably knowledgeable Catholic. I had previously discussed a similar situation with a serious and knowledgeable Catholic friend - not a source I can link to, but that is where my understanding about "living as brother and sister" as the Catholic approach to dealing with the mess comes from. The Canon law page linked above confirms the necessity of protecting children in any decision.

The confessions (e.g. Westminster Confession) of most Protestant groups are just as strict about divorce - there are different approaches to dealing with the messes caused by divorce and remarriage. The practice of these ideals has deteriorated horribly in all communions, including Catholic.

We all need to repent - Holy Marriage is the divinely chosen living illustration of Christ and the Church. 2 Corinthians 11:2 Revelation 19:7-9 When marriage is defiled, Christ is obscured.