I think, for me at least, the difference in this one situation is that she can have the kids, is supposed to, but just doesn't want to "parent-up".
For example, during our marriage any time there was a problem with a babysitter it became my problem. Especially during summer. If the babysitter left the house messy, I had to counsel her on it. If she let the kids be couch potatoes, I had to counsel her on it. One time where a babysitter was, for some reason I'll never understand, lighting matches just to watch them burn I was the one who had to terminate her services. Mind you I had to do that over the phone from Atlanta because my W refused to do it.
She hates conflict and hates standing up to people. Not that I love it but I'm an executive by trade and that's part of life.
So in this case she has hired help in the house. Help that I am paying half of by the way. All she would need to do is sit the babysitter down and say "I need to be left alone. Please keep the kids downstairs and engaged. Here are solutions for keeping them engaged. If all else fails take them to the pool, the park, for a walk, downtown, or whatever."
But she refuses to do that because she doesn't like the conflict. Instead she keeps running downstairs to set up the crafts, takes them to the park with the sitter, etc...
When something outside of her control comes up or even if she just wants a break we have an agreement that we check with each other first. Because she works the weekends when she doesn't have the kids usually she can't, but usually I can since I don't work weekends. Same with weekdays and weeknights.
But to me this was really more of her wanting me to accommodate her unwillingness to handle a situation in an adult manner. To fall back on how things have always been... she's uncomfortable with a problem, then the solution is to have me solve it for her.
But she doesn't want a caretaker, so she says, and I've realized (and still working on) that caretaking isn't a healthy relationship base.
Married 6 together 8 Me:38 W:31 second marriage for both SS12, SD10, S6 Bomb: 9/8/11 (day before our 5 yr ann) W moved out: 2/18/12 D final: 11/12/12 Share S 50/50. Spend as much time as I can with SS & SD