Time to make a escape plan if you really need or want to get out the situation, but i wouldn't go homeless unless it's an emergency, we don't know your full situation
Sign up for housing authority.
And in the meantime, while you watch this develop, generate friendships and connections. You sound very isolated.
Is there more of a problem with him than what you said before - that he gives his first child more attention than the younger two children you have together?
If that's the worst of it, I think you shouldn't make you and your children homeless because of that.
If there's more to the situation, and it's endangering the children to live there, that's a different story.
For some reason, he connects to your daughter in a way he doesn't connect to his baby sons yet and that may change.
You have absolutely no family at all? Like even if they were a state or two away there is noone? If not there are shelters that can take you and your kids. There are group homes for single mothers and or expectant mothers. Is he abusive, or on drugs? If he is one or both then call the cops and have him removed from the home for the night so you can get things prepared to leave.