Ignore this if it is unwanted advice, but I've been in "dramatic" situations myself and want to say this.
Your dh, from what I've read in your previous posts, has not been reliable or consistent in your marriage. You've stated many ways you've attempted to meet the needs of the children and keep the family intact. You're the one with the steady income, the one that bought a house, and the one who is worried about making things work. Perhaps your dh is as well, but I've not felt that to be the case from your posts.
You're also now the one who is considering losing that home and trying to make a place in your life for a stepson you barely know, who comes with some added pressures in the form of behavioral issues. Bless you for thinking of this child, for wanting to take him in and for trying to make his Christmas (prior post) as happy as you could.
BUT...please consider carefully what will happen if your dh decides again that "he isn't in love with you anymore" and wants a divorce. Where will that leave you as far as financial security? Custody? I wish with all my heart that there was an easy answer and everyone could come out of this with a happily-ever-after story, but the reality is that you have a difficult path ahead of you. Think carefully about what this will mean for you and your children who live with you now; it may be wise to consult a counselor who is familiar with these types of issues and can give you a better idea of what things you must deal with and the potential ramifications of the various actions you can take.
I would be very hesitant to try and make this work if your dh is not on board 100% and doing everything he can do to expedite things. I am concerned that he is (apparently) willing to let you make these sacrifices for his son when, as far as I can see, he has not taken any steps until now to take care of this before it went into crisis mode.
If you do decide that your stepson needs to move in with you, find out how you can best ensure that his mother can't swoop in and take him away again at her whim. I don't know anything about that but don't take for granted that it couldn't happen.