No, if she'd written that, she'd have received sympathy.
Instead she tried, sneakily, to paint her daughter as uncaring and unfeeling by specifically pretending that her daughter said: "we really don't need her anymore....Not really for better jobs---we just think it would be cool to live there. AIBU to think this is our right to do this, and that my Mum should approve?"
OP apparently is incapable of theory of mind, she can't in any way put herself in her daughter's shoes or try to imagine how her daughter thinks and feels, and instead she has centred herself in the narrative and tried to paint her daughter as a villain.
The daughter would have a completely different story to tell and there are undoubtedly excellent reasons for the move, that don't centre the OP. But we will never hear them, because she's attempting to manipulative the narrative and has from the very first post.
When someone behaves quite cunningly, as the OP has, in order to try to paint another person as a villain, that tells you a lot about them and nothing about the person they want to paint as a villain.
Perhaps there are very good reasons why the daughter has moved far away.