I came from a family who travelled a lot because of my dad's worked. I went to 13 schools in total, so yes, it was extreme. To be honest, I hated it, and so did my sister and brother. They suffered terribly with the moves with regards to schools. My brother always found it hard to make friends as he wasn't one to want to socialise, and my sister always struggled academically.
My dh & I refuse to move away unless it is absolutely necessary. I just couldn't my kids through what I went through.
However that's only my story. I really feel you need to do what's right for your family. If the kids really want to be living with their dad, then perhaps that's probably the best solution. But do keep an eye out for when you see changes in them, that maybe it is getting too much with all the moving.