Go back to your divorce attorney or some other attorney that practices family law and act now. File in the same Court that granted your divorce. Discuss custody modification, contempt, how the UCCJEA will play into your case and emergency relief. Don't wait another day. Go now. There are too many facts, issues and questions for a free, on-line Q&A.
Your new spouse would not have any liability for the old house debt. However, if you and new spouse have joint accounts and the ex is not making the payments, the mortgage company can come after you which would include accounts in your name or joint accounts if your name is on them.
While it is an unusual arrangement, if you both agree the Court may very well approve it. Logically you could each pay support to the other when it's the other parent's month, there could be no support paid due to having them equal times, or you could compare incomes and have the parent making the most pay a reduced amount, accounting for the time they have the children. Trying to get approval of this type of custody arrangement would best be done with an attorney representing you. Also, you...
No Court appointed attorney.
You may contact
MS Legal Services tel:1-800-498-1804
Or, Volunteer Lawyers Project tel:601-960-9577
Go see an attorney to find out your rights. Most will work with you on a payment arrangement.