The point is not to drive back and forth, but to relocate.
Especially in this case where the end result was that she ended up just crashing on her daughter's couch, moving down to Olympia or whatever to rent out some questionable super cheap room somewhere seems like it would have been a much worse decision. Perhaps she was just waiting long enough to justify "giving up" and having to rely fully on her daughter.
Why are you so defensive about the mere existence of a homeless person?