Bats' whole "that alien princess" attitude toward Kory has always been weird to me. I mean, he may not approve, but this is/was a definitive relationship in his "son"s life as well as a fellow member of the cape fraternity, you'd think he'd have forced himself to come to some kind of terms with her existence.
Maybe he didn't like the fact that by definition she opens Dick up to the existence of not only a world beyond Gotham, but an entire universe? Bruce does tend to like his little Batlings deeply rooted in Gotham. (Why else would Jason stick around, after his training tour of the world and his Countdown tour of the Multiverse?)