It's slightly different for me as it was my Dad who was in the RAF but from a childs perspective, I can't say it has had any real effect on us. He would be posted away for usually 3 months at a time, which would sometimes be extended while he was there. Usually to The Falklands, Italy or Bahrain and we would obviously all stay at home with Mum. The only time it was difficult for us was when he was away over xmas or your birthday. In terms of moving around, I was quite lucky as we moved a few times when I was very young but our final move was whilst I was in my first year of school. We moved to RAF High Wycombe and stayed there until he retired, then stayed in the general area since then so I've got fairly solid grounds but I do feel for my older siblings. They were moved around so much, sometimes to other countries that their education was a bit screwed up. Although things might have improved since those days.
One of the things I do remember of his time in the RAF with good memories is sending blueys to him when he was away. There was a rule in his section that the person who received the most blueys in one weeks would have to buy the drinks in the bar for the night for everyone else. Knowing this, we used to write out letters out, one word per bluey. Between 7 kids and a wife, that works out to be quite a lot of blueys. He's kept a lot of them because they're probably the most heart felt things he will ever receive. It was also fun being a RAF brat. There were so many functions in the mess's, I remember it as a really good time.