I completely fail to see how Bruce being all tender with his own kid somehow cheapens his character. What? He can only bond with boychildren with whom he shares the bonds of personal trauma?
It's not his being tender with his own kid that cheapens the character. It's the fans' claim that, because Bruce is being tender with the kid, it must mean that the kid is his. The implication is that he couldn't possibly be tender with a kid that is not blood-related to him.
Besides, at this point, I think we're supposed to believe Selena's already told him the father is Red Herring Slam Jr.
He is Batman. Whatever Selina told him, if the kid is his, he knows it.