] LR seems to think this is why Anne does not like Bath.

I think there is another reason Anne does not like Bath - it is where she is sent after horrible things happen to her. Not only would it have reminded her of her most painful memories of grief over her mother, she was sent also after her broken engagment.

It would have also reminded her of that period. With those two associations (I had never picked up the second till this GR), I think her distaste for it is reasonable. Or at least understandable - everyone is allowed to be irrational about such things. There are places, movies and songs I hate merely because they bring up bad memories.

] Who would not be depressed, losing a mother at so young an age, being left to a self-consumed father and sisters, and being sent away from her family after such a loss?

I'm not sure what to think about this - but I imagine she was sent away for her own good more than becuase she was unloved. I speculate that LR arranged it. (I have NO proof, I know - it seems like something she would suggest).

Perhaps it was thought it would be easier to be distracted and move on somewhere new where Anne would not be constantly reminded of her mother. People often think this.