If the other side does not respond to a request for negotiation? ; if negotiation does not come to an agreement?

チルドレン・ファースト
You can use the Proceedings for Conciliation of Domestic Relations in a family court. These proceedings are a process in which a judge and conciliators mediate any disputes between parties with respect to issues of divorce, child support, child custody, etc.

In the event that no solution is reached through the conciliation procedure, the process transitions to the Proceedings for Adjudication of Domestic Relations where a decision will be rendered by a judge upon the conclusion of formal legal proceedings