I was 'dragged' around the world and I am fine
Seriously ... IMHO it is all about mindset. If you see it as being 'dragged' then that is exactly what it will be.
I have no recollection of feeling like I was being pulled/dragged. My parents told us we were moving and we moved.
BUT ... I was lucky. I was able to spend my whole secondary education in one school (a British School overseas) - my siblings (all older than me) were moved as teenagers and I think they suffered. But then again, I had friends who would come to our school for 2 years then go off again and according to our Old Students website they all seem ok.
My parents had many friends whose children went to boarding school as they travelled around the world with their work. My father was against this and was of the opinion that if the job meant going to a place where there were no decent schools then he wouldn't take it. Being with us was more important than some swanky job.
Fast forward 25/30 years and I seem to have found myself having a bit of a nomadic lifestyle myself - we moved to NZ when DS was 2 and 5 years later have found ourselves in Melbourne, Australia.
To start with I was against it as I was hoping to finally set down the roots I never had as a child. But I eventually got my head round the idea.
Of course, the schools in NZ and Australia are fabulous so the education side of things isn't a problem .... But DH and I have made the decision that when DS is coming up to High School age we need to settle in one place until DD (4 years younger) finishes school.
Re locating teenagers isn't the best thing (from the experiences of my siblings) and boarding school is just not an option (my thoughts are 'why have kids?' and DH, who went to boarding schools says, 'over my dead body')
So ... imho, if we were in your shoes, we would either take them with us OR DH would find a job that meant staying put for a few years. Boarding school would not be an option.