I’m uncomfortable with the fact that an arbitrator can basically ignore the law. Is this true?

True, an arbitrator need not adhere to the law completely; if the arbitrator makes a mistake of law or a mistake of fact, this will not provide a basis for refusing to conform to the arbitrator’s decision. Again, however, the participants to an arbitration are free to determine the extent to which the arbitration will adhere to the law. This relates very much to your rights to appeal an arbitration decision. If the arbitrator does not understand the law, or does not adhere to the law and a decision is made contrary to what would have been made in court, you may be stuck with it.

Say my spouse and I enter into arbitration for a dispute on a divorce agreement. What happens if my spouse ignores the arbitrator’s award? Arbitration isn’t a court, so what can I do?

While arbitration is not a court, in those states that have adopted the Uniform Arbitration Act, arbitration acts in a manner like a court for enforcement proceedings. That is, if your spouse should ignore the arbitrator’s award, you do have recourse to a citation for contempt. Of course, you would have to obtain a court order for the enforcement.