I actually think that this is really quite harsh.
The banning seems inappropriate as she hasn't done a lot wrong besides argue and use swear words (which a lot of people do here).
Posting the PM she sent you in this way is just degrading and humiliating and to be honest childish. There is a reason why they are called "private".
Just let people be how they want to be and quit trying to change people (other than making them better players).
Just bring it, lol
