I'm basically grasping at straws.
I searched and can't find the previous posts about your agreement with him. Is there a signed document stating terms? Are situations like terminating the agreement covered?
Also, remember that he's caused you a great deal of grief, I hope he's completely repaired the damage to your daughter's vehicle he incurred while drunk.
And less than a month ago you said:
And it's a cracked heating exchange. We get to replace our furnace less than a month after moving in.
If you've paid any part of that, you should expect him to pay you back, either in free rent, or cash, or take the stupid thing with you when you leave (actually don't, in the absence of a contract it would be considered destruction of property).
If you have a contract, particularly a rental contract (if it says "rent" anywhere in it, then state rental laws probably apply) then you have a LOT of protection and options.
If you don't have a contract, you still have a lot of protection and options, he can't just kick you out - but you can leave without notice and stiff him any rental fees he might suppose you still owe.
Getting an apartment after foreclosure is hard, but not impossible:
https://www.thebalance.com/how-to-find-an-apartment-after-foreclosure-961001
Getting another apartment isn't easy, and you will have to make a number of big sacrifices, but at this point I think you need to focus on getting your family out of this bad situation and into a stable (though undoubtedly uncomfortable) situation quickly. Look around for a 3 bedroom apartment that's cheap - less than 1/3rd your income. Plan on staying there for a year. You might have to save up a month's rent and a damage deposit to convince the landlord to rent to you ("Yes, my credit is bad, but I can pay you a month in advance on top of the damage deposit"). Look for smaller rental companies or individuals renting units rather than companies and large rental groups - smaller ones will be more likely to accept risk.
Then live there for a year, pay your rent exactly on time, get receipts for those payments so you can prove to your next landlord that you're capable of maintaining your housing costs.
Small, uncomfortable, and annoying, yes, but you have to rebuild your credit and your ability to eventually buy another home. Further, it'll be additional pressure for your children to figure out how they're going to support themselves, and it'll be a good example to them of pulling together your family and resources and bouncing back slowly and steadily from bad situations.
I do think you'll have to let go of the idea that you can settle down. You may have to make a lot of sacrifices in convenience and comfort. But I suspect that you'll be better off giving these things up and maintaining control over your situation than trying to work things out with ex boyfriend outlaw and maintaining the tenuous status quo.
If you do have a rental agreement, have him make out receipts for each of your payments that include the date and amount so you have some evidence to show other landlords regarding your capability to pay. They won't put much stock in it since it's a personal relationship, but it'll be something and you can show the withdrawals or cancelled checks from your bank backing up the movement of money. It'll be better than nothing.