(not trying to be snippy, I'm just trying to understand how this is okay and how her taking away my parenting influence during days I am supposed to have them is okay)
Let me flip this around.
At work, I can change my schedule around so that I can be at lunch with them on "her" days. Not that I would EVER do this. But from your logic, it's okay. Let's also pretend that she actually makes them lunches. (Before I filled up their school account with money for buying milk (and they use it to buy lunch on her 2 school days), I was dropping a lunch at school for them every morning, including her days because if I did not, she would not take any responsibility in feeding them or taking care of keeping the school account up to date)
Anyway, what if I show up every monday and tuesday, throw her food in the garbage and bring unhealthy crap for them to eat.
edit: Also, I could probably get a note from the doctor if I absolutely had to and took it to court. They have documented nutrition and growing problems.