Makes sense. I'd encourage you to have a good talk with your partner to see how each of you can give the other time to step away from parenting guilt-free. It's important to find that, for both of you. It might sound silly to ask them to give you three hours to play D&D, but it's not. This is actually even more important to do if you feel you have a parenting situation that neither of you can step away from, not less.

I've been in the same situation with LoL and parenting in the past, letting down a 5v5 group, so I totally understand the hesitation. My problem was that I was trying to sneak in the time instead of being honest about what I wanted from myself and my family right then. It's just about being more intentional with the time commitment. And recognizing that D&D is much more forgiving of unexpected surprises than MOBAs are--the GM can always say you're off running an errand or just roll for you if you have to leave during a combat. You'll find many groups are forgiving of being a new parent.

Also, keep in mind non-parents also have things come up. It's not just us. My D&D session Saturday night cut short by two hours because the GM thought he had recovered from a Friday night migraine, and he suddenly realized how tired he was. We had been planning the night for two weeks but it was totally okay to wait and plan a time to resume. It's all normal.

I was trying really hard to avoid giving the OP any specific advice on their personal life when I wrote my comment higher up, but now that you've posted I have to chime in: yes to everything you said.

Being a parent, much like being a married, doesn't mean you stop being your own person. Everybody needs time to do their own thing, away from their partner and children; as much as we love them we also need to take care of our own wants and needs.

So yes, absolutely, speak with your partner and figure out some time you both can step away guilt-free. And keep in mind that groups are more than willing to accommodate your needs.