Yeah, if TDK was years later, he would have gone up against the Joker several times already since learning about him at the end of BB. Yet TDK feels like Batman's first Joker case, and when they arrest him it's certainly the first time it's happened.
The Gordon's child thing is just a big old continuity error - deliberate, too, they just ignored that the child we saw in the first movie was a baby and made it many years older - that's what the do on soaps and sitcoms too.
There's a lot of confusion about Barbaras in this thread though, man. That's Partly Frank Miller's fault for stuffing it up in Y1 by calling the wife Barbara and omitting the daughter.
Anyway the baby in Begins is NOT a Barbara - it looks like a boy, and presumably is supposed to be James Jr. The only "Barbara Gordon" in Begins is the wife.
As for the Neice/Daughter thing, it's either/or. Daughter pre-crisis, and (stupidly) neice adopted as daughter post-crisis. Gordon doesn't have a Neice AND a Daughter named Barbara.
And Sarah Essen is in no way whatsoever any version of Barbara's biological mother. I'm not sure Gordon ever even had children with his second wife. She's only Barbara's step-mother.