Yes there can be language that if she misses a payment then the car gets turned over to you. You need to discuss this issue with your lawyer for more specific advice for language to include in your decree.
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The family law court cannot force a refinance. It can enforce a "hold harmless" provision in your marital settlement agreement or a direction that she turn the car over to you if she misses a payment. "Repo"ing the car is a remedy only for the lender. If it is in both names, then you have as much right to it as she does until family court intervenes, but just to take the car and leave her without transportation could be a very bad move in the eyes of the family law judge. This needs to be handled right. Consult with a lawyer.
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