She has a lot of arguments she uses for custody, but only one that is real.
Negative, Ghostrider; the pattern is full.
That's not a "real" argument, epistemologically, ontologically, phenomenologically, or juridically.
That's not even an "argument." Let us recall Philosophy 101: An "argument" is composed of two or more propositions, a premise, and a conclusion, logically related to each other such that all of the propositions lead to the conclusion, with the transition between premise, proposition, and conclusion comprising the inferences upon which the sum -- the argument -- rests.
What she's got there is a premise that (as you correctly identify) boils down to "daytime employment does not equal parenting capability," a category of premise which is known in the advanced study of formal logic as a "bullsh*t" premise, which comes, of course, from the Latin for "droppings-of-a-bovine-male."
More problematic, her premise is also her conclusion, a logical fallacy scholars call "total bullsh*t," from the Latin for "droppings-of-a-herd-of-bovine-males."
There's no incentive at this point that I can see -- not that I have any particular vision -- to be cooperative, insofar as the mediator and/or her lawyer are concerned.
Just keep documenting your time and expenses vis-à-vis the kids. And you might consider having your lawyer ruffle a few feathers and inform her lawyer that you are considering filing an Order to Show Cause why she should not be subjected to a vocational aptitude evaluation by a court-appointed vocational counselor -- a common-enough procedural request and one which will put the kybosh on this idea that she's just going to float through without pulling her weight.