He should actually be thrilled that the family gets to do something so cool.

You call this trip a once in a lifetime trip, but really it isn't. You never know when opportunities will arise. He's the one who's on a once in a lifetime adventure. He shouldn't begrudge your trip.

If his mission gets messed up because you go on this trip, that is 100% on him, not you. He'd have some repenting to do. But don't sell him short. Missions make boys into men, and I'm sure he's on the right path.