Fight what system? How? She gonna sue the JSA? She doesn't "cave in." She gets mad, for one night, and decides to go to the party, for one night, before she reapplies herself to the problem. On her way to the party, she discovers a new option: be Batgirl. She takes it. How is that "giving in"?
She doesn't 'obey' him when she hides things behind his back.
Behind his back. That's not even remotely the same as confronting him, taking actual irrevocable steps to actively and directly oppose him. And not in some empty after-dinner argument. In a long-term, very serious way. You say "she's an adult" but she's not. She's an eighteen-year-old in a society that expects us to be emotionally and financially dependent until we're twenty-three and structures our psyches accordingly. Babs saying "fuck you Dad, if you're going to stop me I'm going to get the law on my side," you really think that's an easy, automatic or appropriate behavior for an eighteen-year-old who loves her father? Seriously? When you bring the law into a family dispute, you're talking things like divorce, emancipation, child services, domestic abuse. You want Babs to bring that kind of intensity to her close, strong, loving relationship with Jim, before exhausting every other option? Particularly when "every other option" includes something as incredibly easy as "put up with Batman's bullshit"?