I hear this fairly often in parent time and visitation matters where things are not working out well. The usual complaint goes along the lines of: "My husband and his ex-wife have been constantly in litigation about various child custody and child support issues over the past few years. It has taken an enormous toll on us."
That shows that the other person is not following the orders, or prior agreements. Instead that person is doing exactly what he or she wants and forcing you to either agree, or face more conflict. In other words, you're in a high-conflict case.
The bottom line answer is yes, you can agree to use arbitration or mediation. But each requires an agreement with the other party, and is the other side going to cooperate?. Arbitration is just like trial, for each problem you will need another hearing.
Mediation is a method of negotiations, movement on issues, and settlement. I have nothing against mediation to settle a divorce, but I do not see using it to address these kinds of problems. Mediation opens the door to renegotiating your custody and parent-time orders.
Why should you do that? You already have orders in place, and the other side is causing problems. Do you really think the other side is going to suddenly agree to abide by the orders? Or is the other person going to push to change those orders to be much more favorable to his or her desires?
There is an alternative; you can have a special master appointed to your case. That can be done either by agreement of the parties, or by a court order (based upon a motion by one party). The special master will then be joined into the matter to handle all of the disputes and issues you raise. You can use your attorneys with the special master, or the parties can work with the special master. The order appointing the special master will specify the powers of the special master, and both parties do have the option of taking any matter to the judge. Ultimately the judge has the final say in any matter, each party has the right to go to the judge (and subsequent appeal), a provision which may not be available with arbitration.
The advantage is that the special master works on your case, and can provide decisions within days, not the weeks involved in going to trial or arbitration.
I have been trained as a special master, and have recently been appointed to handle such cases in both Utah County and Salt Lake County.