1. Can you plan for a worst case scenario if H does cut off support? Visit your bank and find out if you qualify for a loan of some sort. It sounds like it's just a matter of time until you have a well-paying job, so the security of knowing there is a source of funds to carry you through if you need it might help you be less fearful. You may also be able to get a loan for retaining an attorney. Another place to query is women's organizations in your area. I do think that H is emotionally abusive (and potentially financially abusive) to you, and with a newborn and your schooling, I'm wondering if there may be some funding or legal help for you through organizations that assist women in tough situations.
2. I don't agree with your parents that you should be twisting yourself in knots and putting up with whatever H wants to throw your way in order to have him not yank support. I feel like it's torturous for you, because you aren't able to make empowered decisions. It is a matter of time until you don't have to worry about finances, so you just need a stop gap in order to not have to rely on keeping H happy with you.
3. On H's end, there may be more to his coming home late and sleeping there. Hey may be reluctant to follow through on leaving and sleeping elsewhere due to what that would mean for custody. Also, I think he thinks it keeps you holding on/happy with him if he's there and not sleeping elsewhere. If H is looking to buy a home, he is likely applying for financing, and child support payments might inhibit that process. So he may be playing a game where he's "technically" home, and paying money, but as soon as he gets a place he may cut you off. What I'm certain that he doesn't want is for you to file for child support, because it's a dose of reality and may inhibit his ability to buy a home.
Really think about that last one. H also knows you have a well-paying job in your future, so it is to his benefit to drag this out and not have you file. That may be driving his behavior. I do also think there is an element of controlling you, here. If he's there every night, he knows what you're doing, he ensures that you can't exactly move on with your romantic life, and he holds onto a connection with you.
I am with OwnIt in thinking that there is zero reason for you not to start the 90-120 day process for support and custody arrangements now. I don't think playing nicely is going to get you anywhere, given that he has a history of cutting you off financially, and I think the current situation is very advantageous to him and not so much for you (outside of finances, but you can think outside of the box there so you're not relying upon his good graces.)
T, having a bit of knowledge of how you view situations, I personally think what holds you back is fear. Fear of being cut off financially, certainly, but I've addressed that in the points above. I also think you fear permanency, given your emotional thinking regarding H purchasing a home (how he was really "done" if he did that.) If you file for support, then it's permanent and you and H are divorcing and that's it. In reality with only logical thinking, that's not necessarily so. It means you would not be shielding H from the direct consequences of his decisions, which is perhaps the best thing for him to start re-thinking his choices. The best thing about it is that you'd be showing via your actions that you accept his decision and aren't trying to control him: you're letting him go, just like he wanted.
