Saw it today and agree. Most of that beginning was well done and would have been a good start to a batgirl movie but it had no business being in TKJ. This is a joker story, so I don't care about what's happening with batgirl. If they wanted to pad length, how about showing what Joker did after falling in the chemical vat and going crazy? I always thought of him wanting to pay a visit to everyone who had wronged him before.Legality isn't the issue, it's poor characterisation. Plain and simple.
Barbara's end of things makes sense. I get why there's tension, I get why she'd have a moment and make a move to jump his bones. The problem occurs when Bruce doesn't say "no". It's out of character and only happens because someone on the production crew *really* wants to see Batgirl f*ck Batman. That's very poor story telling. Doubly so since literally none of this has anything to do with the rest of the movie. It's entirely separate.
Overall I give it a C+. Not bad but could have been so much better without that batgirl anchor dragging it down.