“He still wanted me to stop seeing you.”
Here see means to meet or spend time with someone. Although see someone can mean to date them in American English, here the boyfriend wanted Tina to stop meeting Frank. It does not mean merely looking at him.
“It's him or me.”
It's A or B. can force a choice between two alternatives. Tina's ex-boyfriend demanded that she choose Frank or him.
“You don't get to choose my friends.”
Don't get to … denies someone the right to decide, more explicitly challenging their authority than can't. Tina firmly says that choosing her friends is her decision, rather than his.