I think either King doesn't know Selina's character or he doesn't particularly care because this is about Batman not Selina [my guess is the latter]
About King bringing something new to Batman.
Much Like Grant with introducing Damian / Talia and her occ rape of Bruce. Selina is being twisted to serve this Batman story. I'm not a catwoman expert but no Catwoman i know would tell a child/future stepson that. [Actually Injustice Selina would but that Damian was older and an enemy]
so far Selina, the boys, Duke, Holly and Talia have felt like mere plot devices.