While I agree with everything you've said whole heartedly, by law H has the right since he pays C/S to have reasonable visitation time with his children. He really doesn't spend a whole lot of time with them.
Many, many here send their children with their spouse knowing full well the spouse is living with the OP while still married to them. Many here hate that fact, but by law there's not a damn thing that can be done about it.
My L did say that my children were old enough to make up their own minds about whether they want to meet ow or not. I'm praying that D does not want to go, but preparing myself if she does.
This is one sitch I can't control. I'm learning all about those.