Advice please


I'm five months pregnant.
Recently I discovered my husband was having lots of long phone conversations with a girl I'd never met. They met online, said they were just friends, etc. I told him to knock it off. It continued. He started sneaking around and hiding it from me and it escalated. He was lying to my face every day. I moved out. Lived with a friend for a few days. Life was hell. He has finally kept his word and stopped calling her, but she continues to call him and he continues to talk to her. I've talked to her twice and told her unequivocally to stop. It came to a head on wednesday. I came home, we talked. He admitted he doesn't love me anymore. He's been feeling this way since before we actually got pregnant, probably before we even started trying but he never let on in those months. He says he wants me to stay but can't give me a reason why he would want that or how I could possibly trust him, what he would do to try to turn this around.
It doesn't make sense financially or logistically for me to kick him out. I'd be left alone with a new baby and would have to put her in daycare (no) so that I could work full time. That was never the plan. That was the point of waiting till we could afford to live on 1-1.5 incomes for a while. One of the points anyway. Also, I'd be left with an unfinished house that I would have no hope of finishing myself, and no way of selling it until it is finished.
My parents have offered to take me in, but that would mean putting grandma in a home (needs to be done anyway, badly). Much of their house would have to be redone, painted, new floors, because Grandma in her senility has destroyed the place, their whole house in fact would need to be cleaned out and prepared for a baby and room made for us. My parents would be losing the income from her SS - and they refuse to let me pay rent other than chipping in on utilities. In short it's a major burden on them. But they want to do it and are willing to watch the baby for me while I'm working, which is the important thing.
Yes that should be Mike's job. But I don't trust him.
When I ask him "Why should I stay?" it's like the answer "So I can be with my daughter." doesn't even cross his mind.
I don't want to leave him. I still love him as stupid as that is beginning to sound. I missed him so much when I stayed at my friend's house. I cried every night, though I'm doing that here too, but at least here I can see him and he can hold me. He still does, even though he says he feels nothing.
I said I would stay if he would get some therapy. I've yet to get an answer to that proposal. I doubt I will. Or I'll get an affirmative but he won't really go.
If I tell my parents I'm coming home, it's one-way. I can't go back on the deal without being a real bastard. They weren't planning on putting Grandma in a home until it was absolutely necessary or my mother retired. (4 years).

So I basically have 2 undesirable options that I can see... stay with him and see what happens, or leave him and move in with the parents.
I'm not sure which option would be more miserable.
But I can't just take this one day at a time either. I have a baby coming very soon. I need a place for us. I need stability.

Brilliant solutions? Ideas?