A psychologist may give an opinion about custody. Most divorce cases are tried before a judge without a jury. Once it is signed and notarized by both of you it can become grounds for divorce if you live apart for one year after it is signed and if you both follow the terms of the agreement. You are still married after signing the agreement. The time that you and your spouse live apart does not start to count for the one year required to use separation as grounds for divorce until the agreement is signed.
Mediation is a process of settling a dispute without going to court.
You and your spouse meet with a neutral person who will help you to make decisions about your legal matter. The mediator facilitates the discussion, but has no power to make a decision. The result is a written agreement which may become a legal Separation Agreement or could be read into a court record and incorporated into an order signed by the judge. Mediators charge by the hour. There is an additional cost for preparation of the agreement.