There are two issues here. The fact that he clearly wants to spend time away alone with his children, and the way he's gone about doing it.
I go on holiday alone with my kids every year and the reason why I do it is because I can then give them my full attention and it is much more enjoyable for me this way. When we all go together, I find myself under pressure to give them and my OH equal attention, having to deal with the fact that both want to do different things to fully enjoy themselves.
It works for us perfectly though as DH also goes away skiing with his friends once a year (sometimes twice) as he has done for many years even more he met me. However, we also make time for the two of us to go away twice a year for long week-ends (these are our xmas presents to each other) and every few years, we will make it a week.
The issue with you is that the dynamics of holidays have not been discussed yet and I expect from the perspective of your OH, this is because you haven't moved in together yet so he still considers your two families as distinct enough to make such decision.
You say you are planning on moving in together so this definitely needs to be clear before you do as as you're experiencing currently, resentment could take over otherwise.
Don't resent him for wanting to go away with his kids only, but do point out that for the sake of your relationship, you should also be arranging to make time to go away just the two of you. I do agree with you that arranging this just after your big birthday certainly lacks thoughtfulness and in your shoes, I couldn't help questioning his commitment to a long term relationship with you.
I assume he is taking them that week-end because of the school holidays, but since you'd be talking about doing something together for your birthday, his decision to go ahead and book something at that time without talking to you about it first is quite uncaring indeed.