A very common issue that arises in divorces is removing a parties name from a joint debt. This can arise in the form of a jointly owned automobile, home, or a simple credit card.
How do you get your name off that debt?
The simple answer is you cannot. The judge does not have the power to affect a creditor's rights in collecting a debt from whomever is listed on that debt. Imagine if a judge in Texas could change the names on a jointly held credit card of a company in New York. A Texas judge does not have that authority.
In the case of a jointly owned automobile or home, the only way to clear the other parties name off the debt is to either get the loan company to agree to do so (fat chance), sell the item and buy something new, or refinance the home or car in question. If none of these are an option, then you are most likely stuck with your name or your ex's name on the debt.
With credit cards, the same goes as above. You can ask the credit card to remove one parties name or, to be safe, you can pay the debt yourself.
Can you get the judge to order them to pay it?
Yes you can, and the Court has the authority to order one party or the other to pay it. What you have to understand, however, is that does not change the fact that both parties names are still on the debt. If the party ordered to pay defaults on payment, the creditors are going to seek payment from BOTH parties regardless of what the order says.
Your only recourse in that situation is to ask the Court to enforce their order that the party pay that specific debt. In Texas, even if you prevail, the judge cannot put someone in jail for failure to pay a debt so the best you could hope for is a judgment against the other party. A judgment is not worth much for someone that has nothing. Collecting a judgment in Texas is a tough proposition.
The result is that you are left with trashed credit or you are out the money to pay the bill that the other side was ordered to pay.
The moral to the story is, if you are concerned about your credit, pay the debt. If it is a house or car, refinance or sell it because a Court cannot affect a creditor's right to collect their debts.