According to Collins,
If you put up with something, you tolerate or accept it, even though you find it unpleasant or unsatisfactory.
During the entire period of her growing up from being a child into an adult, her parents and brothers had to tolerate/endure/bear her rude and inappropriate behavior or tolerate her meltdowns, lack of communication, carelessness, etc.
Collins says "something that is prickly feels rough and uncomfortable, as if it has a lot of prickles. Someone who is prickly loses their temper or gets upset very easily" (like teenagers). Cambridge defines prickly as "complicated and difficult to deal with."