H.W.
I think you need to reexamine the divorce decree and any limitations regarding moving/how far away you can take the kids.
Otherwise, personally, if you could find a decent school district in the area you would be working, maybe this would be good? I don't know. I also don't live in SF or LA or wherever you might wind up. I do know that you should consider certain aspects of life there; both cities deal with massive amounts of traffic and the cost of living is more expensive than it is up here in Portland. (My only frame of reference.)
Sounds like a lot of research is in order, including child care, etc. But the divorce decree is the first thing to examine.