What is the test that determines doctrine from discipline?

Let’s start of by saying what the Church teaches [= Doctrine] regarding communion for divorced and civilly remarried Catholics:

However, the Church reaffirms her practice, which is based upon Sacred Scripture, of not admitting to Eucharistic Communion divorced persons who have remarried. They are unable to be admitted thereto from the fact that their state and condition of life objectively contradict that union of love between Christ and the Church which is signified and effected by the Eucharist. Besides this, there is another special pastoral reason: if these people were admitted to the Eucharist, the faithful would be led into error and confusion regarding the Church's teaching about the indissolubility of marriage. – Pope St. John Paul II > Apostolic Exhortation > Familiaris Consortio, 84, November 22, 1981.

And

Today there are numerous Catholics in many countries who have recourse to civil divorce and contract new civil unions. In fidelity to the words of Jesus Christ - "Whoever divorces his wife and marries another, commits adultery against her; and if she divorces her husband and marries another, she commits adultery"[Mk 10:11-12] the Church maintains that a new union cannot be recognized as valid, if the first marriage was. If the divorced are remarried civilly, they find themselves in a situation that objectively contravenes God's law. Consequently, they cannot receive Eucharistic communion as long as this situation persists. For the same reason, they cannot exercise certain ecclesial responsibilities. 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. – Catechism of the Catholic Church, CCC 1650.

Understanding Doctrine to be Any truth taught by the Church as necessary for acceptance by the faithful [Cf. Dictionary: Doctrine | Catholic Culture] and Discipline to be … any of the laws and directions set down by Church authority for the guidance of the faithful [Cf. Dictionary: Discipline | Catholic Culture], the words of the great and saintly pope in his Apostolic Exhortation can be read as However, the Church reaffirms her practice, which is based upon Sacred Scripture, of [the discipline of] not admitting to Eucharistic Communion divorced persons who have remarried.

Another scriptural passage on which this teaching is based is:

28 Let a man examine himself, and so eat of the bread and drink of the cup.29 For any one who eats and drinks without discerning the body eats and drinks judgment upon himself. - 1 Cor 11:28-29 (RSVCE)

Returning to the question, is the not admitting to Eucharistic Communion divorced persons who have remarried to Eucharistic Communion doctrine or discipline? It is both doctrine and discipline. Doctrine because this has been the Church’s practice based upon Sacred Scripture and it is discipline in the sense it is one of her laws and directions set down by Church for the guidance of the faithful.

It is good to recall here that the Supreme law in the Church is the salvation of souls [cf. Can 1752]. If the Church were to admit to Eucharistic Communion divorced persons who have remarried but who are not living as brother and sister, she herself would then become the vehicle of leading to damnation not only these persons, but also all the faithful who would be led into error and confusion.

To the question is it possible to have invincible ignorance when it comes to receiving communion in an invalid marriage?

Perhaps a father confessor can better answer this but in this day and age and its means communication and their ubiquity, chances for that are very slim.

I can see those civilly dicorced and remarried receiving communion, not so much from invincible ignaorance, but because it is what everyone does, as a result of poor catechesis and because of lax and bad clergy, etc.

The short answer is that doctrines are truths, whereas disciplines are practices. Doctrine can be known, whereas disciplines are actions that we need to do.

Moreover, doctrines merely reflect the reality that God has entrusted the Church to teach the faithful (the so-called deposit of faith). In other words, the Church does not invent doctrines; she merely reports them (much as a scientist does not, or should not, invent his findings, but merely states what he has observed). On the other hand, disciplines entail a specific decision by the Church to act in one way and not another.

Here is how the Church defines “dogma” (which includes those doctrines that have been solemnly defined by the Church, or else are so fundamental that one cannot deny them and remain Christian):

The Church’s Magisterium exercises the authority it holds from Christ to the fullest extent when it defines dogmas, that is, when it proposes, in a form obliging the Christian people to an irrevocable adherence of faith, truths contained in divine Revelation or also when it proposes, in a definitive way, truths having a necessary connection with these. (Catechism of the Catholic Church [CCC] 88)

Although there is no “official” definition of the term doctrine, in Church documents it is generally used to mean truths that the faithful are obliged to hold, which includes, evidently, the dogmas, but also less central truths which the Church has definitively proposed. (Have a look at a 1998 motu proprio called Ad tuendam fidem and the commentary by then-Cardinal Ratzinger, especially no. 9.)

Likewise, there is no “official” definition of discipline, but it always entails certain practices, such as the Western Church’s practice of choosing only celibate men for the priesthood.

For example, the hot-button issue discussed in the synod that has just closed—regarding the possibility of admitting couples in irregular marital situations to Communion—has to do with several important doctrines:

1. A consummated, sacramental marriage (a marriage between two baptized persons in which the marital act has already taken place) is indissoluble by any human authority whatsoever. Only the death of one of the spouses dissolves it (CCC 1612-1617).
2. Attempting a new marriage when one is already married is gravely sinful. (By definition, it entails an act of adultery; see CCC 1650 and 2380-2381.)
3. Receiving Communion when one is in the state of grave (or “mortal”) sin—i.e., when one is not in friendship with God—is a sacrilege (CCC 1388, 1415; see also 1 Cor. 11:27).

Note how, although these doctrines include moral precepts, nevertheless they are simply statements of what the Church knows about the natural law and the nature of marriage and the other Sacraments. They are not things that Church has had to decide; she is merely transmitting what our Lord has given her to teach.

On the other hand, the current practice of the Church is to withold Communion from those persons who engage in publicly and persistently in gravely immoral actions:

Those who have been excommunicated or interdicted after the imposition or declaration of the penalty and others obstinately persevering in manifest grave sin are not to be admitted to holy communion (Code of Canon Law [CIC] 915; see also the 1994 document by the Congregation for the Doctrine of the Faith regarding this issue and Familiaris consortio 84).

Note how this is a conscious decision by the legislator, directing the Church’s pastors to act in a certain way. Of course, this discipline follows quite naturally from the doctrine. Although the Church could change her practice somewhat, she could not do so in such a way as would blatantly contradict the doctrine.

For example, the Church could find new ways to facilitate the process to investigate the nullity of previous (attempted) marriages (as the Church, in fact, has recently done with Mitis iudex Dominus and Mitis et misericors Iesu), or else find ways to move couples in irregular marriages to repentence (for which the first step, doubtless, is making sure that such couples know they are not excluded from the Church and should feel a part of it, even while recognizing the irregularity of their situation).

Simply admitting couples in irregular situations to Communion, however, does not seem to be compatible with the doctrine.

Dogmas are truths proclaimed either directly by God or by God through His Church. That one cannot and should not receive Communion in the state of mortal sin is not a changeable discipline but a dogma of the highest degree, de fide.

The 24th Session of the Council of Trent says:

Canon VII.—If any one saith, that the Church has erred, in that she hath taught, and doth teach, in accordance with the evangelical and apostolical doctrine, that the bond of matrimony can not be dissolved on account of the adultery of one of the married parties; and that both, or even the innocent one who gave not occasion to the adultery, can not contract another marriage during the lifetime of the other; and, that he is guilty of adultery, who, having put away the adulteress, shall take another wife, as also she, who, having put away the adulterer, shall take another husband: let him be anathema.

Now,

1. adultery is a mortal sin (cf. Matt. 19:9).
2. Divorcing and remarrying is adultery.
3. Therefore, divorcing and remarrying is a mortal sin.

He who receives Communion in the state of mortal sin, i.e. "unworthily…shall be guilty of the body and of the blood of our Lord. … [He] eateth and drinketh judgment to himself, not discerning the body of our Lord." (1 Cor. 11:27,29).

Living in sin also causes more sins: scandal, temptation to other spouse to commit adultery, and a grave injustice to the children.