I know not everyone has this experience, and my mediation wasn't binding, but when I divorced my first husband (who was not an A), our mediator (who was also an arbitrator) was literally the FIRST neutral, outside person who took one look at what was going on and immediately grasped how totally ridiculous my husband was being. It was a profound relief in many ways.
My hope is that you have a similarly wise arbitrator, and that you are able to work out a solution that protects the kids AND your peace of mind.