I've always found Bruce and Kate's relationship slightly creepy since they became cousins. By all implications it looks like he only brought her into the family to keep her under some level of control, and influence her behaviour. Thematically this is problematic.
Add to that he kept his uncle locked-up in the Belfry, he might keep his cousin locked-up in his Batcave after she takes over the Colony.
For that matter Bruce and Kate have known each other longer than anyone else in the Team (since childhood), and they definitely don't agree.