Can a judge be contacted after a trial when the opposing party is refusing to follow court orders?

You cannot contact the judge directly.  The proper procedure to deal with someone who is violating a court order is to file a  Motion requesting that the opposing party appear and show cause why they should not be held in contempt for violation of the court order.   If the court finds that they willfully violated the court order and that they have the ability to comply, the court can hold them in contempt of court, and depending on the type of contempt, may imprison them, order that they pay a penalty, and order that they pay the aggrieved party's attorneys fees.