Her children need the stability of school, so I'd be saying no to holidays during term time. Unless, exception of course, trip of a lifetime/family bereavement.
I would say she should be saying co-parent. Because Dad is very much in the picture. She full admits kids are with Dad some of the time/they share custody. They do not sleep in her home every single night, and other parent doesn't just see them on a Saturday afternoon, for example.
I know parents who are not together, who do not interact much, but still call it co-parenting. (I don't know the full story, but impression I get is they co-operate very much for the sake of the kids, despite not liking each other at all.)