My employer allows us to have children around in the school holidays, providing we get our work done. Because they understand that not everyone has the family support to assist and that holiday clubs for the full six weeks is expensive etc etc.
If the children being around was impacting someone's work, they'd have a conversation with them about managing it better or not having the kids around.
I've been with this company nearly a decade and, to be honest, you'll have to pry me out with a crowbar. Because they actually care about their staff. And because they do, their staff care back.
Previous roles (with managers like you) I would log off/walk out on the dot regardless of what still needed doing or what issues arose. Not my problem once you stop paying me, because you don't see me as your problem.
Here, I don't clock watch. If some days I need to do an extra hour or so, I will do it. If I need to log on and check things on a non working day, I will. Because I know they have my back too. I would walk over hot coals for my line manager and our head of department. And they know that, so they won't ask me to.