Okay. Look. First of all. It's not babysitting when it's his child. Bruce gets that. He's raised a bunch of kids by now, and it is kind of insulting to have it inferred he's 'babysitting' when it's his kids. As if Alfred's the 'proper parent' or something just because it's assumed that a rich guy isn't gonna do his own childcare. It's 'babysitting' when Alfred watches the kids! ...Except it's not because he's basically Grandpa at this point, but. Point stands.
Anyways, the important note is that Bruce is fully capable of taking care of his own children. ...Yes, they're usually older. He usually adopts, like, ten and up. Actual small children, he has less experience handling. But he's still a father, and he can still look after his own kids, darnit.
Maybe he's in a bit of a tiff about it. Alfred had fussed a bit over leaving him alone with his newest - and youngest - today as if it would be an imposition. Granted, Alfred also fusses about leaving Bruce alone in the Manor in general. ...Admitted inability to cook for himself aside, ahem, Bruce is fully capable of handling a day of domestic duties. And spending the day with his child? One of the better ways to spend a day, really. He's fine. He's got this.
Granted, maybe he'd... underestimated, how rambunctious small children can be. Maybe he'd failed to rein it in, just a little bit, when the chance was there. Maybe he'd bit a tiny bit scared of coming across as too intimidating, setting a bad precedent for one-on-one time together? Trying a little too hard to be 'fun'?
Look there has to be some explanation for why he has essentially allowed himself to become a jungle gym right now. Or perhaps a ladder. He's got an energetic child climbing on his shoulders, and he's yet to put a stop to it, one way or another.
"Careful," he cautions, trying his best to hold still and resisting the small, protective urge to set them right back down on the ground and do the 'high shelf reaching' himself. This is kid behavior. It's normal. Right?