Tough spot. I personally wouldn't be satisfied with that arrangement and would probably say something like (ccing mediator):
"We're making decisions that will be very important for our family's future. We've agreed to try the route of mediation as it's never ideal to turn over control of those decisions to a third party such as the courts. That said, for mediation to continue to be a viable option for me I would need to see us improve in our communication. This would mean getting responses to the emails I've sent and having replies phrased with a respectful tone. I'm open to feedback on what you may need from me to make this more effective as well. This is an emotional time but I'm still willing to set those feelings aside for now as we work together for our children's best interest."
That's assuming it was TRULY bad behavior (and not simply you being mad at her for being mad at you). If it was just irritating and frustrating I'd put up with it. If it was hostile and uncooperative I would not. But the way I wrote this up wasn't judging, blaming, or controlling. It was simply a boundary of what I would and wouldn't put up with.
Vets- I'm curious how you feel about this.
Me:38 XW:38 T:11 years M:8 years Kids: S14, D11, D7 BD/Move out day: 6/17/14, D final Dec 15