Her abuse narrative is par for the course. This comes up in one way or another in the vast, vast majority of WW-initiated separations. You are the one who is feeding this garbage by constantly bringing it up here, in counseling, in your head or wherever else. And talking about this in any way in front of a counselor is a monumentally stupid thing for you to do. You really need to never, ever entertain or discuss this topic again. Ever.
I can tell you something - she doesn't even believe this or else she would actually take action against you, but instead all she does is use this to beat you into a corner. I have seen WW do this same thing with wild accusations against their nice guy husbands when the WW is literally dating sex offenders. And I don't mean I saw this once, this happens so much its cliché! This abuse narrative is her best, most effective weapon against you. That is all it is, and you are the one who keeps sticking your nose on the barrel. If OM wanted to take her to Hawaii for 3 weeks she would happily drop the kids off at your place on the way to the airport.
I understand you have a lot of anxiety and fear. You can either tackle this fear head on, or hide. I don't think you are ready to face it, so I suggest you hide. I will tell you how, its really easy! Get a note card and write this down:
Message received: 1-logistic information 2-delete
Message sent: A- "kid pickup will be at X:XX o clock at XXXXX location" B- "noted" C- "I will refer that to my lawyer"
Then, from now on you should not say a word to her, all communication in writing. When she sends you something, decide whether it is type 1 or type 2. If its type 1, then you can respond with either A, B or C.
I'm not even joking about this. I'm completely serious.