I am an 'Army Brat' born and bred Army, from birth - 18yrs old
Its a slightly difference point of view and one that i know you didn't ask for, but i thought i would let you know it from the kids point of view...
'Forces children are more socially adaptable to meeting new friends, joining new groups etc because they have to do it' This is SO true. We moved every two years and this meant, house country and schools. The regiment my Father was in, meant we moved on our own, but the vast majority of regiments moved together, thus enabling kids to move with the same kids IYKWIM.
However, it was fun, it was exciting, it was an adventure, i got to have a new house, new bedroom, garden, shops, parks, neighbors (not always the best but overall good!) There was a sense of 'newness' when i started schools, but this was what i was used to , i loved 'choosing' my new friends, sussing out who was who and who i was going to sit next to. I never once found it hard to strike up a conversation or make friends, and the great thing about forces schooling, is that EVERYONE is in the same boat, so there was never a 'them and us' situation.
I wont go on and on, i am sure you dont want a year by year detailed account of my life...but until you have lived it and experienced all it has to offer, you (civilians) don't understand. I think what i am trying to say is, don't worry about taking your kids with you, if that's what you decided to do, try not to worry about other people who knock the idea, it is your life and you need to live it the way you see fit. I would say though, make a decision and stick with it, there would be more confusion swapping their lives round if you chose forces life then went back to civvy etc etc etc.
Hope that gave/gives another perspective?