Hugs, TC.
I know I've had similar conversations with some of my family members, and it is often difficult to understand just where those comments are coming from. They aren't always about you, like you said with your mom's general feelings regarding cats. But, it's really difficult to not taking discouraging comments like that personally. My (socially inept) aunt asked me a few years ago, while my entire family was standing around my newly-deceased grandmother in the hospital, if I regretted moving out of the state for grad school because I wasn't around her very much for the last few years of her life. What the heck was that about?! I have not really forgiven her for that insensitivity, but I do know that it stemmed from some warped insecurity within her that has actually nothing to do with me. I'm still working on not taking it personally.
Also, my brother commented on some potential financial drawbacks this last time I chose to move out of the state away from my family. Your sisters comment reminded me of that. I think he was just trying to come up with a reason for me not to move so far away. I bet your sister likes having you nearer. Maybe that's all it is?
Peace,
Fathom