Originally the young Barbara who became Batgilr and Oracle was Gordon's niece and I think she got adopted later? Barbara was Jim's wife and if I'm not mistaken she was pregnant with Jim jr in Year one? Jim jr disappeared later for ages and popped back up in Black Mirror.
I would recommend reading Batgirl Year one (and Robin Year one too) btw. It won't set this straight (although it goes with the niece version IIRC) but it's a really damn good story, lots of fun (but very different to year one).