DS can very mature one way but also suffers from anxiety and depression. I think would welcome being away from us for 3 weeks. I went away recently and DS loved it
and DH is away constantly so being away from family is normal for us (also all our family live on the other side of Australia so being on our own is the 'norm').
As for money, I actually have a holiday saving that I'm more than happy to use on DS. I just went OS for a short break and fixed my need for a holiday. Plus I'm starting a new job next year so I'll only be able to have holidays in the school holidays and I hate travelling then.
I think if it's under 5K I'd jump at the experience. It might help DS grow. I'm actually excited for him ! lol Think of all the study I can get him to do dangling the trip over his head lol.
DS loves history so I'm sure he would learn a whole lot from the trip. DS actually wants us to go to England and France on our next holiday just to go to all the historic points of interest (plus Warhammer in London!!!).