I, also, know a few things about move-aways and changing jurisdiction. Because I did both.
In the situation posted, move-away was granted, and that was never really a question. Yes, I made a comment about OP moving her child away from Dad, but that did not detract from the fact that OP had the court's permission to do so.
In MY situation, my moving *with the children* was a stipulation of the settlement. Had I actually REFUSED to move away from my kid's Dad? We would have continued a full, blow-out, contested custody case. I'd said all along that I would happily stay in the area as long as he did. He moved shortly after, so I guess he had an inside scoop I wasn't privy to. And therefore, jurisdiction was changed - although my current state wasn't keen to accept it. It was my ex that pushed it. Go figure.
ETA Oh wait... he didn't realize that CS would remain based on the originating state's laws.