Define what you mean by canon? I’m not exactly sure what you’re asking here, oops :S
It wasn’t an episode. It was in the companion series of comics that they released. I’m not sure what issue it was … I think #20? Or #21? I’m pretty sure it was the last issue of that series!
Nightwing #1/2 - “The Scott Breaks”
written by Chuck Dixon
art by Scott McDaniel & Karl Story
I’m not Batgirl. Not tonight. Not Batman’s star pupil, as I used to be. Not the girl who did everything right… who danced through Gotham and dazzled everyone she met. Tonight I am Barbara Gordon. She of the eidetic memory. She who never forgets. Never. - Batgirl #01
Personally, I stay far, far away from anything regarding the children of my ships because none of them feel right. Sometimes even the canon versions weird me out a little. I don’t even keep my own headcanons because I’m never satisfied even without them. I think the only one I can think of that made sense was John in the Lords Universe of Batman Beyond.
I have to say, I can see why someone would want to name a Dickbabs child James. But at the same time, I don’t know if they will because while Babs’ father’s name was James too, people always called him Jim. And the person she — and probably Dick too — thinks of at the mention of the name James is her brother who is … not pleasant. So, I don’t think so, but I’m no expert! It can be whatever you want it to be :)
I don’t recall her baby-sitting him in the official sense, but I do recall a panel from Devin Grayson’s run on Nightwing — I think it was Nightwing #86? — where Dick really did seem a bit juvenile and the reader might’ve thought that Barbara felt like a baby-sitter at the time.
Mostly it’s just fanon!