Ann Walker is also very wealthy, Ann Lister did comment on this in one of the earlier episodes,
Apparently, AL did use AW’s money to repair and improve Shibden Hall.
I think that the locals are so used to Ann Lister’s ways that they accept it. She grew up amongst them and seems to have been well liked by her peers on the whole.Also, the uncle left everything to her because he knew that she had the strength of character to manage it. In those days, few women would have been able to stand up against the other business people who were then all men.