Would you switch your kid schools?

Maybe this isn't something to switch kids schools over but my son went through a break up in March. His ex girlfriend is his English teacher's daughter and she was very upset about the break up. My son broke up with his girlfriend. She was upset to the point she was talking about the break up in my son's class and even to other students when my son wasn't in her class. Several students actually went up and told my son that she keeps talking about them and their break up. Another parent went to complain before I did because she found it inappropriate. Last day of school she told my son in front of the class "Just so you know, Mia got a new boyfriend." I told the principal and she sighed and said she's been talking to her about that. My son will have her again for English and honestly she's too unprofessional. Even if my son did something horrible like cheated on her when is it ever appropriate to talk about teens to other teens like that? I don't understand.

Edit: DAUGHTER DAUGHTER HE DATED HER DAUGHTER!!! SORRY!