I'm sorry OP, his father and his new partner should be taking all their children with them on holiday. I agree with the PP who says others are tying themselves in knots to justify it but it's always the child that loses out.
I dont think it matters who pays (even if that's the new partners family) if there isn't the money to pay for all of them, don't go. That's what would (should) happen in a biological family set up, and a blended one should be the same.
If you choose to become a blended family, you can't pick and choose who to take with you, it's cruel.
I feel the same way about doing something special on a weekend that all the children would want to attend (a theme park for example). I think you should plan it so all the children can come. It's just basic consideration for people's feelings.
No, I don't feel that you should sit at home doing nothing on other weekends... I mean doing something out of the ordinary and that all the chidren ould enjoy.
Likewise, I'd be upset if my friends planned a get together without me on a weekend they knew I couldn't come, knowing full well I could have if they'd done it the weekend after. It would feel like they didn't care if I was there or not. Which I imagine is exactly how these poor children feel.