Neither party is required to agree to anything they do not wish to accept. A mediator may be able to predict how a judge would likely rule on each issue, but cannot force an agreement. But an agreement forged in a mediation can contain imaginative solutions that a court may not be allowed to make on its own. Also, even if the entire case is not resolved in mediation, often there are only a couple of items left for a court to decide. Next time you have a dispute that could become a court case, consider going into a mediation with the other side.
Many counties now have dispute resolution boards.
The American Arbitration Association is another source, and a local attorney could either do the job or tell you how to find a mediator.