Reading the letter, I think the real issue for the LW is feeling put upon by a long list of things their sister has needed help with (note that the LW didn't step in on the house issue until the police became involved and that nobody suggested returning those several pairs of expensive boots and putting the money back into paying for the sister's expenses).

The LW doesn't want to spend time with their sister, and I really, really don't think that over-tipping is anything but a very ragged fig leaf of an excuse for walking away and not putting themself out to help on the bigger and more difficult stuff.

If the family is in the US, it would be extremely easy for the LW (or for someone completely unrelated to the family) to take legal control of the sister's finances without her consent. (Last Week Tonight did an episode on this. As with most of their segments, I only recommend watching if you have the mental/emotional resources to be horrified by human behavior.)