If Sierra and her mother had a good relationship, opening her bag (isn't it more of a book bag anyway vs. a "purse?") wouldn't be a big deal. If they have a strained relationship then I could see where it would be intrusive to the teen.
THAT SAID...if I had a teen that was troubled, I would make it clear that I would be searching everything and anything and at anytime of my choosing. As an adult I see it as my responsibility to know what is going on and keep a child safe. Sometimes you have to cross those privacy boundries. Once behavior improves and trust is earned, then slowly the lines of privacy can be restored. This is just my approach, and JMO.
Regarding the mother...well, she's definately offbeat, but that really doesn't matter. Her personal style isn't at question here, just her forthrightness. As far as her giving Sierra money every day vs. once a week....well, perhaps she's not sure how much she's going to have day in and day out to give?
Despite the mother's unusual communication style, one very positive thing stands out. I recall Sierra (in one of her online comments) complaining she was sick,and was SO annoyed because everytime she coughed, her mother would holler out to make sure she was o.k. Now that isn't something a mother who doesn't care about her daughter would do...