A good mediator can often help a parent look at the system more realistically. Sometimes it can be resolved by eliminating the battle over the label and instead looking at when the kids will be with each parent. There are two ingredients in settling one's case. First is to know what you want, and the second is to look at the other person. But you only need one person to make changes and to try to end the war.
Many people end the war unilaterally.
In some states you can request and get an order for mediation, but often if you are dragging someone there, it is like trying to force a horse to drink water. Unfortunately, courts and legislatures are rarely looking at studies or even what the psychologists say. Joint legal custody should work in most cases, even if people can't get along. Rarely will they say you can't make joint decisions unless there is real detriment to the child. However, the real danger is with the joint physical custody.