I'm not reading Wonder Woman, but if she's getting a kid *too*, I'm going to laugh a lot, and possibly write playdate fic. Maybe prophecy told Diana that Kon wasn't supposed to die in IC, so she spent a year in Hell bringing his soul back, and now he's a cute Konlet with disturbing Oedipal tendencies. He can get even more disturbingly attached to Damien out of vague memories about dark-haired mini-Bats, and hug him while Damien desperately tries to nerve-strike him through his aura ("The Heir Of The Batman Shall Not Be Called Timmy-poo!"). Chris just ignores them, being too busy changing the diapers of Selina's daughter, while Sin and Lian watch TV and laugh at them.
And speaking of likely events, Cass can become sane and babysit them.
Or Tim. Unca Tim taking care of all of them would be awesome. ("Think strategically, Damien. If you kill me, Kon will go back to trying to hug you, and being a god-human-kryptonian hybrid, in a few years he might be developed enough to try to mate with you." "...You are good, fake brother. When I become the Batman, you shall be my Robin." "Whatever. Now put the knife away and eat your vegetables.")
On the other hand, Cass as a governess... *goes to the Special Shallow Hell* She'd turn the bi-weekly assassination/kidnapping attempt on the boys into a play/training situation. And given her history, she'd be *nice* with the kids. She might actually be uniquely suited to control Damien - she has the assassin training, she is possibly somebody Damien's teachers told him to be wary of, she understands what kind of fucked-up upbringing he had, she can *read* what he's feeling, and she'd have no problem kicking his ass as many times as needed (prediction: a lot at first, then less often, then a huge lot when he hits puberty and his entitlement complex makes his foot a permanent inhabitant of his mouth; hell, knowing Cass, maybe literally).
I intensely dislike bloodline inheritance of heroic or leadership roles -I have problematic elitist tendencies, but all meritocratic, thank you very much- so I don't like this OYL baby boom, but... well. We'll see.