I was a 13 and 14 year old boy once (at two distinct points in my life as it happens to be). If I were you I would either approach the owners of the magazine (parents or daughter) and explain as nicely as possible that these magazines DO represent an influence whose influence I would rather minimize on my pubescent children. Especially at this age where hormones have only recently come into play and can be quite confusing, you can’t be sure yet where your children stand on these issues.
I’m a little unclear why “mentchlichkeit” is taking priority over what can potentially be devastating spiritually negative influences. If there is room to to have both, then great. But if not, this can potentially have very bad consequences and from my own experience I would give it major priority.
I understand that the daughter has anger issues, I have a sister-in-law in a similar situation as this girl. But I don’t think it is proper to tip-toe around her at the expense of the children.
Be courteous, but stand up for your children. You’re the only one who can.