Can a judge force you to accept mediation?

Might depend on the situation. Sometimes judges are given the final authority over approving a mediated agreement. Do you have an attorney?

Court rules in some states make require binding arbitration or mediation in certain cases. If that is the case, then the parties are bound by the decision of the arbitrator or mediator.

It all depends upon the state law and any court rules adopted pursuant to those laws.

Consultation with an attorney who has experience in such cases would be highly advisable.