Court-issued divorce orders are legally binding, and courts have the power to compel compliance. If your spouse refuses to abide by the modified agreement, one option is to file a petition to enforce. If granted, a petition to enforce can force the offending spouse to submit to the order, on pain of legal penalty. The noncompliant spouse could be subject to fines, administrative penalties, or, in cases of continued refusal, criminal contempt charges.
For instance, say the noncustodial parent refuses to comply with a child support modification to make larger payments. The custodial parent could file a petition to enforce the order. If granted, the court could use several mechanisms to compel support payment, such as garnishing wages or seizing tax returns.