Except that Babs never set out to join the Bat-clan in the first place. She originally made her play to join the JSA. Specifically, she wanted to work with Canary, and ended up running into Wildcat who basically told her "That's not how we do things." Dinah turned her down first, and it was only after that, that she got into a big slump, needed something to break out of it, and got the idea of going to that costume party, wearing a -Bat- costume.
Why a Batman costume? Because it would piss off her Dad, who she was really interested in antagonizing after he'd told her for the billionth time "No, you can't join the GCPD."
I never got the impression that she was looking for validation, so much as that the men in her life (Jim and Bruce) could seriously -prevent- her from doing what she wanted to do. As a fairly prominent cop, Jim had pull. If he really wanted to, he could say "Don't let my daughter join up." Would she hate him for it? Sure, but if he was sure it was the right thing, he could do it. And as for Bruce, well, he could take a more direct approach in keeping her out of the vigilante game. It just so happened that he -didn't.- Sure, he made a big show of making it look like he was trying to push her out, but there are multiple points in the miniseries, where we see that Bruce is actually pulling strings (He's playing bad cop, Dick is playing good cop) to make sure that if she doesn't succeed outright, at least she stays safe long enough to realize she can't hack it.