I'm not a bitter single mum DH and I are together. But I think it's shit to use 3 weeks of your leave to not see your kids, to be honest.
I imagine the children's mother could not and would not take 3 weeks off parenting to go on a lovely adult holiday!
He already only has them every other weekend, and he gets loads of time off work apparently, so he won't lack for holidays.
It sounds hard-line but I believe if you have the terrible misfortune to not live with your own children, you have to accept that you have made a huge life error and you must live with its consequences.
Anyone can get divorced and relationships break down, but in terms of your children, you have to accept your part in fucking up a core bit of their stability, and therefore it's now on you, to go the extra mile, to spend as much time as you can with them.
We'd all love a jaunt with a great new sexy spouse with no kids wouldn't we? But once you have had children, adult child free holidays tend to be off the table for the time they are young, for both parents. And the more so if you are divorced. The greater needs to be your effort to stay close and have multiple touch points through every single week of their lives.
Maybe this is a one off, this holiday. But it is statistically likely he doesn't pay the real costs of taking care of them, he doesn't do their life admin, he doesn't have them that many days in total.
So, hearing about a luxury American break would piss me off too, if I were the children's mother and daily holding myself to a higher standard of care and being present.
Also. New wife, wind your neck in. "No we can't come visit, dear family, for three weeks, you know DH has young children and it's too long for him to go without seeing them" is what you should have said. Maybe he doesn't get that holiday, you signed up for that when getting together with a man with children.