I guess I don't get the "sexist" angle with Barbara at the beginning. I mean, the big thing of it was that she initiated the sex; and Batman's trying to sideline her was -seemingly- due to his feelings for her and wanting to protect her.
I do agree that the two parts aren't blended together well and in order to do that you'd need to take the actual TKJ part and make some changes, but I think that's allowed in any adaptation. They change I would suggest is that while Barbara is unconscious in the hospital, Bruce kneels next to her bed and opens up to her saying something like:
"I'm sorry I put off talking to you after that night, I was letting my feelings for you cloud my judgment. Everyone who has ever gotten close to me has had to pay the price in some way or another and I couldn't bear the thought of that happening to you so I kept pushing you away, hoping it would keep you safe, but I wonder if doing so didn't just put you in more danger."
And then she wakes up it being left open to interpretation on whether or not she heard him.
More probably could have been done to tie the two segments together, but the opening act was pretty much necessary to establish Barbara as a character rather than just having her show up for two minutes in the beginning of the movie only to get shot and be unconscious the rest of the time; pretty much a "woman in the refrigerator" moment.
But we got to see her passion in the beginning as well as how she's able to kick as much ass and "go to that point" like Batman and what led to her retirement as Batgirl, but I don't see the sexism in it. It's not uncommon for workplace romances to lead into one sheltering the other by restricting their work actions if one is a subordinate to the other or for the romance to cause workplace conflicts; which is why workplace romances are often discouraged. But it's important to note how Barbara was the aggressor in the encounter and, slight, argument could be made she forced Batman into it. (Yes, I'm suggesting that.)
As I said, I really liked it. I might temper by grade a bit in hindsight after a day or two of cooling off from seeing it and reflection, but it was entertaining. I liked seeing Batgirl kick ass, I liked Conroy and Hamil again in the iconic voice roles and The Killing Joke is just one of the more iconic stories that needed this adaptation; though it could have been better. It was really nice to see something of an "origin story" to The Joker and to have him humanized a bit. And to see the suggestion that he was always on the brink of insanity since, as Batman points out, Jim Gordon remained sane after being pushed to the edge so for Joker to have gone nuts when faced with that edge he must have taken himself to that edge. Batman himself even managed to stay on that ledge.
In the TKJ part, it probably could have been fleshed out more itself, I had always gotten the feeling that the mob had killed The Joker's wife and unborn child as means of dotting all of their "I's" and it would have been nice to have seen that shown here, though maybe that's changing too much.
Again, I thought the movie was great and I enjoyed it and I think it's getting too harsh of criticism, particularly the first segment and the romantic liaison between Batman and Batgirl. They're both adults, Barbara in her early/mid 20s, Batman in his late 30's/early 40s. Bruce is a handsome, powerful, billionaire and Barbara is a hot, 20-something, woman. Seems like a romantic encounter would almost be unavoidable if they were working closely together for long enough.