Update: I am returning the dog. Thank you so SO SO SO much to everyone who gave me advice, you are the only reason I felt brave enough to go through with it. Thank you for letting me know this was the right thing, not just for our family, but for the dog. I just got off the phone with the head of the rescue, who sounded devastated. He hadn't even read my e-mail, and glanced at it while we were on the phone, saying:
"This is all fixable. Everything here sounds totally fixable if you were willing to put in the work. These are just leash-training issues."
I said something along the lines of, "I believe that the walking issues are fixable. I even believe that her aggression is fixable. But I don't think the middle of a busy city is a safe place for her to be working on leash training. And I don't think a home with a cat who is now getting sick from stress is a safe place to work on aggression. Her life is at risk when we go outside." (Like, clearly he didn't read the part where we almost got hit by a car?)
It probably wasn't that articulate and was definitely said through a trembling voice. But I guess the message got across, because he just said in a totally crushed voice, "We'll send someone out. We'll be in touch," and hung up on me.
I feel very sad and I'm going to miss her a lot. I'm also not looking forward to the hand-off, both for the "saying goodbye" part and for the inevitable shaming and emotional blackmail from whoever I bring her to. But thanks to your guys' words of wisdom, I am now convinced that, no matter what they try to make me believe, I am doing what's best for the safety and happiness for all involved, including this gorgeous dog.