It is absolutely disrespectful and unprofessional for a T to check messages during a session. Unless there's a real emergency of some kind, the phone should be silent. I think it's also disrespectful and unprofessional to be routinely late, as it sounds like this T is, unless the client is okay with that and the time gets made up. You are not overreacting and you are in the right.

Worst of all, she is treating you like your feelings about this don't matter, and that is profoundly disrespectful and not at all therapeutic. It is damaging. You have another T, sounds like, so I'd say ditch this one.