My exh and I used a mediator, but we also each had a lawyer. Mediators cannot legally advise; their job is to draft the divorce agreement. The lawyer is to advise each party if they're ceding too many rights.
Over the years here it's seemed your H has been a bit of a control freak about many things, so this is not going to be any different. Well, to be blunt, he has given up the right to tell you how to conduct your personal affairs moving forward, business, romantic or any other. You are under zero obligation to do things his way. In fact, you could be actively jeopardizing your future if you do so. He is not rational and he is not looking out for anyone's best interests but his own.
In terms of the children, I didn't tell my son it wasn't mutual. I let my exh spin his BS, and when our son asked me, I just kept saying it didn't matter who made the decision, it wasn't going to change anything and what was important was that we both still loved him and he was the priority.
Son of course quickly figured out what was really going on. There's a lot of tongue biting and word weighing that goes on to make sure you're honest with the kids, but not parentifying them, i.e. turning them into the confidant, saying things like "you're the man of the house now" etc. That's where damage comes from.
I wouldn't want the kids to see a fight, so I'd personally deflect, chose my words very wisely and neutrally, and let them figure it out. This is H's 'stage' let him perform on it. Just be your authentic self. When you're alone with the children you can answer their questions more openly, i.e. your father has made his decision but I think saying that in front of stbxh will only serve to stir the pot in front of the very audience you're trying to soothe.
just my $.02
M 20+ T25+ S ~15.5 (BD) BD 4/6/15 D 12/23/16
"Someone I loved once gave me A box full of darkness. It took me years to understand, That this too, was a gift." ~ Mary Oliver
