It takes two people to make a marriage work. I went down the counseling road for two years and listened to my ex mouth polite lies and never follow through on his promises.It does not sound like your husband really wants to work on this marriage. That doesn't mean he doesn't love his kids- but it sounds to me like he doesn't want to be married.
I had no money and getting separated and divorced was the best decision I ever made. We had a difficult couple of years, but now my son and I are doing great and I am getting remarried in June to a wonderful man who has a great relationship with my son and is completely responsible.
If the best reason you can find deep in your heart for working on your marriage is based in fear for what will happen to your house, then that says something right there. Your kids may be little now, but as they grow, they are very smart and observant and will see what's going on.
My son was in preschool when we split up and I made a real effort to keep his schedule the same, etc. even though we moved to a small apartment. He came through it really well and still has a regular relationship with his dad. DO NOT put your kids through living in a toxic environment where the parents fight or just can't stand each other. They will know!
The good thing about splitting up when my son was young, was that by the time he was in elementary school ( he is going into 4th grade now) we all had a 'system' We had a schedule of weekends with dad and weekends at home, we could meet at soccer matches, school conferences, etc. and be polite and pleasant to each other. He has remarried and all four of us can be in public to support our son. Having the time to work all that out while he was smaller and get used to it really really helped.
Go see a good family lawyer. Chances are very likely that you would get physical custody (that means the kids live mainly with you) and child support of course.In that case, you would very likely get to stay in the house. But even if you can't- it is just a house. YOU are the mom- make a HOME for your children where ever you are!! Love and support is what matters most.
See a mediator and work out a detailed schedule for when your husband would see them and how it would work. It is all very very hard at first. But in the end, you will be so much happier and stronger if you do what you truly feel is best for you. Your kids will be too. As long as you are positive and loving to them, they will be fine.
I am giving you my experience just because that was happened to me. I would have the same advice whether I was still married or not. I disagree with the poster below that just because I am divorced, I would want other women to be divorced too! You are NOT a failure if your marriage fails!! You were not put here on earth by God just to keep your husband happy no matter how poorly he treats you. Your first responsibility is to yourself and your children. Don't let other people try and guilt you into anything at all!! Best of luck to you!!!