Sounds like this looser ex is going to be in your life for the next 24 years or so.
One option, if the bank will even take it seriously, is to Refinance. Since he has such bad credit, he won't get financing. No lending institution is going to put such a bad risk on a new mortgage, especially in this climate of sub-prime loan disasters.
If your credit and income will qualify, the bank may let you refinance and put the house in your name only, which then you could turn around and put up on the market if you wanted to sell.
Either way, he has to agree to the refinance. He may want part or all of the equity when you refinance. It would be worth the loss just to get him gone and out of your life:financial and otherwise.
Unless you can refinance, you are stuck legally and contractually with this guy for the life of the loan. You are financially responsible for the life of this loan, should you just move out but leave your name on the mortgage. If you go and he defaults, they will be all to happy to come to you for back payments and taxes.
Without refinancing, don't just let him move out. If he moves out and you stay, he can still come back when he wants to and with whom. For it is still his house -for the life of the loan.
Call your lender and get your options. They are not interested in the details of you life with the looser you picked. In this day of forclosures, tell them you need to refinance into your name only-how can you do that. Most lenders do not want another forclosure on their hands. Once you know a plan of action, and only then, present it to the soon to be EX that you are ready to cut ties-and for the sake of the kids and to help him lighten his financial burden, you are willing to take on the house yourself.
Or better yet, before you kick him out, tell him you would like to lessen his financial burden because you see how much he is struggling and will take the loan on yourself. Once the papers are signed, give him a 30 days written notice of Bye-Bye.
Good luck