According to reformed theology, are _all_ wealthy Christians required to give their wealth to the poor?

Very few have ever thought that to be a Christian means selling all we have and give it to the poor, for even some of the Apostles arguably had a house and did not sell it. At a minimum it is undeniable that Christians owned houses as most Churches were house churches.  This means the situation with the rich young ruler was a specific and unusual case.  It seems to me that Christ's demands of him were equal to his boasts of how righteous he was.  Not to say that this young man was a hypocrite but only miserably ignorant of his true sinfulness.  The fact that Jesus appears to have liked him, makes me think he probably became a Christian later and his sorrow was only temporary.

The man boasts of being so holy, and in his mind he probably was that naive.  However Jesus was about to suffer on a cross and many who followed him would also soon have to arm themselves to suffer. Therefore if this man really wanted to perfect, that is fully take the present circumstances and throw all of his life into what he situation demanded, not only would Christ's command be actually true to meet his claimed desire, but it would also quickly show him how foolish his boast was.

Now regarding your other references about loving our neighbor and how insincere our love is when we hold onto our money while witnessing a brother in need.  There is no trick of interpretation that can reasonably relieve the conscience from this.  However I think this touches on the overall teaching about money and the Christian, which I will quickly share my opinion.

Our life is not perfect, we do not pray as we ought, we do not give as we ought, we are not humble as we ought. If we want to be perfect, or at least grow more and more perfect, we will give more, pray more, be more humble, patient, kind, long suffering, etc.  This will never end in this life.

Therefore, in a sense, yes, so long as we see brothers suffering and we are not willing to lift a finger than we can readily measure how much love we really have.  The ultimate virtue will still not sell all they have, for one must meet one's own needs or else we will never be able to maintain an ability to help other's.  However the general trend of giving, more and more generously is the Biblical view of sanctification in regards to our gifts, which is gradual and steady and not a chore when done by faith.

The weird thing about this is that while the world honors the rich the Bible considering the unequitable nature of wealth in this world, and the moral duty to treat every brother as oneself (a brother always comes before a sinner in ths matter except for one's own family) the rich should consider themselves to have lower external status in the church and greater honor should be given to those who are suffering:

Believers in humble circumstances ought to take pride in their high position. But the rich should take pride in their humiliation—since they will pass away like a wild flower. (NIV James 1:9-10)

Not that we should hate the rich and treat them any less than the poor in jealousy of their external blessings from God, but that all should be treated equally and honor paid to any who suffer which is what in many ways were are called to in order to fill up the sufferings of Christ.

So the bottom line is that yes, if you want to be perfect deny yourself and give your life to others, but be warned you will never be truly perfect in this life and even perfection might mean earning more money to support more ministries and to take care of your ownn family that may also encounter various troubles. 

Basically give to the poor and also save for a day of trial. Proverbs would be of some value here to get the balance. Also for those without wealth, there may be other things we can give that are just as difficult to part with in comforting our brother. Our time, attention, affection, service, teaching, and everything else must also be crucified at some point along the way. Especially our evil unbelief in the love and grace of God expressed in the death of Christ, if we are not willing to part with this and rejoice in the free justification of our souls before God by faith, apart from works, than even if we should give all we have to he poor our love will not be faith filled or real and we will be but a useless noise.

If I give all I possess to the poor and give over my body to hardship that I may boast, but do not have love, I gain nothing. ( NIV 1 Corinthians 13:3)

Of course the answer should technically be "It depends on which reformed theologian you ask", but I hate to leave people confused just because the theologians are...

The context for this passage needs to include the fact that God has been trying for thousands of years to teach us that we need to be loving towards one another and God. This man approached Jesus and asked what he needed to do. Jesus told him to keep the commandments and love others. The rich man said "yeah, I do all of that stuff already."

Now consider for a moment what this man's life looks like. He has amassed great wealth for himself by storing up treasures for himself on earth. Meanwhile, he is surrounded by starving, needy, impoverished people who are in desperate need of daily provision. Somehow this man thinks that he is a loving person, despite the fact that he is hording the very provision that these people need to survive.

So Jesus cuts straight to the chase: "Ok, go sell everything you have and give it to the poor and come join me" He says. And the rich man is suddenly confronted with the one thing he didn't want to hear. You can't follow Christ unless you surrender everything to Him.

There are plenty of Scriptures to support the idea of keeping only what you need, providing for those who are in need, not storing up treasures for yourself, etc. We are just really good at finding creative ways around those parts of Scripture!

Regarding Job, Abraham, etc., it is not hard to find examples of people not doing things in an ideal manner... laughing at God, criticizing Him, taking many wives, telling your wife to lie, etc. etc. Be careful not to take descriptive accounts as prescriptive instructions.

It's important to note that the Mark passage records Jesus telling one specific person to sell all his possessions and give to the poor. Jesus did not give this command to all people in all times.

It is inappropriate to take everything Jesus ever said to any person and attempt to apply it to all people for all times. If we did that, then all of us would be under obligation to go into Jerusalem to get a donkey, throw our nets on the other side of the boat, get out of the boat and walk on water, and fill jars with water in order to get wine.

Jesus' direct command to the rich young ruler applied to that person. Jesus, in His omniscience, may have understood that this man's wealth would be an insurmountable obstacle to his faith. We don't know for sure, of course.

Generosity, as you reference in 1 John 3:17, is, however, commanded of all of those who are rich in this world and who are following Jesus.

It should be noted that a man who is wealthy and continues to grow his wealth over time can actually give exceedingly more and care for more poor people than a wealthy man who gives everything he has at a single point in time.

For instance, a man with $1 million could give it all away at one moment in time and help a certain amount of people. Another man with $1 million, earning a 10% return on his investments, could give 100% of the increase a year in perpetuity. That's $100,000 a year. Ten years later, he's given $1 million and can continue giving for another ten or twenty or thirty years or more.

The command is not to become poor, but to be generous. Money is not the root of all evil--only the love of money.