My heart goes out to you OP, you still see the man you fell in love with and have had kids with, the man you expected to marry and despite all his flaws, you have accepted them and done everything you can to support his recovery and from the sounds of it, have made significant sacrifices for you and your children to support him.
People can recover from this and I whole heartedly applaud your tenacity and commitment to this man. BUT... quite frankly you are damned if you do and damned if you don't here!
If you let him go, he is not taking accountability nor prioritising his families well being. That would be it for me. Its also possible that when he goes, he will fall off the wagon as its too early in his recovery although no one can blame him for wanting to go. And this will; be framed as your fault for stressing him or for allowing him to go when he is not ready.
If you tell him he cannot go, he will rant and probably go back to his old habits and his narrative will be that you pushed him to it.
You need to sit him down and tell him the emotional, practical and physical costs this situation has had on you and the financial long term ramifications for the family. Not only is he not appreciating this, but he is adding to the load by creating additional unwarranted debt . He needs to think about what he is denying you and the kids for his own few days of fun.
I personally would say that just like you, he is an adult and is responsible for his own actions but if he chooses to prioritise his own short holiday at the cost of additional years of financial misery, for his future wife and kids, then he is not the man you fell in love with and the man you have been waiting to re-discover. Tell him you are not willing to do that to your kids and ask if he is?
As a teacher, I am sure you can spot the kids with families like this and you must know first hand how it affects them?
This is his decision not yours, he either starts taking some responsibility for his actions or he needs to ship out. You (or his Mum), can't keep propping him up, he needs to decide to want to do it for himself and sadly sometimes that means he needs to hit rock bottom first...and that is not something your kids should witness.
Big hugs, you must do what you must do as you and your kids will either suffer the consequences or reap the rewards. You have been loving and supportive and now its time to be strong and stand your ground.