This is a major legal question and your SO should get someone to represent him, in court if necessary, ASAP. I would not get a real estate attorney. I would get a trial attorney, or my second choice would me a divorce attorney.
Good luck, I hope it works out. This way your SO still pays for kids to live in house, keeps the house, and payments are a bit lower.
First Weber Group
Certified Distressed Property Expert
Right now it sounds like your SO is in contempt of court and could be arrested if he fails to make the mortgage payments as mandated by the judge. I'm not an attorney so he needs to talk to an attorney asap.
Also because he no longer lives in the house, he may not be able to get "owner-occupant" low rates...not sure how that all works.
Main thing, he need a judge to order his wife to sign the refinance paperwork if he can get in a lower interest rate. His credit will not be destroyed unless he fails to follow the terms of the court order!