I don't think that was a conversation you handled very well.
Actually, I'm sorry to say, I tend to agree with your wife's end of that exchange. You strong armed the conversation by ending the discussion when you didn't get agreement with what you wanted. From my standpoint, I don't think it's reasonable to leave such an issue open-ended when we are talking about a marriage dissolution settlement.
The two of you are divorcing and setting terms for how you will handle issues with the kids. This needs to be clearly defined with as little wiggle room as possible for either of you to take advantage of.
If you really CAN work together, you can still do that within the structure of an alternating arrangement.
You by the way are the one who elevated the rhetoric by throwing in the word "bully." I did not get that impression from what your wife had written.
She of course did over react, but overreaction is pretty normal in an arena like this where emotions are on the sleeves.
All in all, I think you could have handled it much better.
Go back and read the exchange and see how far she moved from her ridiculous position of wanting paid for her time off. She conceded, and then found you unwilling to negotiatie calmly when she proposed a reasonable change.
Maybe the emotions of the issue caused your over reaction?
That's just my take.
BIll
"Don't tell me the sky is the limit when there are footprints on the moon."