Gordon is too straight and narrow.Oh really? There's always another level of depravity to reach! Example, Commissioner Gordon visiting the Bordello to purchase time with Batgirl. All the while with no idea she's the real thing or who she really is.
But Bollock doing it while talking about how she looks like Babs and he's always had a thing for her once she grew up.
Or Sportsmaster wanting to bond with his two daughters.
Perhaps requests Lex bring both to the League of Shadows?