I used to have a great relationship with my academic advisor, and she has been a great mentor to me. However, ever since I mentioned transferring away from my regional institution to a much better school, she has always been unsupportive. Ultimately, I have already made a decision to leave and am preparing for my departure to my new institution, however it annoys me that she will not support me. I feel that a major reason is because her alma mater was at the institution she works at, and she has a deep family connection to the school.
Do I just let it go and move on?
Yes, you just let it go. Stay friendly - you can already tell there’s more going on with her than supporting your education but that’s her issue. And try to resist referring to your new school as “much better” when you speak with her or anyone else at your old school! I hope all goes well with your transfer.