It was wrong to address it on the check to your daughter. Just have your teen call to say thank you and send a thank you note and leave it at that.
However, that weird incident with her was in September, perhaps she had a reason for being upset, maybe it was a small, stupid reason no one knew about, she probably got offended over the course of her stay there, but it was there and she felt she had her reasons, even if they were tiny.
You guys didn't try to call her for Christmas, or say thank you for the check she sent then? If that's true, then you are all just as rude and I think she does have a sound reason for being upset. Your family should apologize to each other and get past it.
take this chance to have a call and sincerely ask her what bothered her, that you are sorry she got offended, but hopes she can see that things weren't done to intentionally offend her, and how you can all move forward and be happy again.