If you're not at a point in your life where you can make a (bi-)weekly commitment with a similar setup, you can always find a DM that is looking for substitute players that can fill in when a regular party member is missing. This is a tactic used by many to avoid cancelling sessions altogether because a player cannot make it, and to keep players on a "waiting list" should a regular need to step out. No commitment on your part is needed and there's no hard feelings if you can't make a game after getting the call because you're not part of the regular group anyway.
Just make sure to find a DM that's understanding of the parental life and if you're comfortable with it you can always give them control over your character if you have to step away where feasible (no DM will want to roleplay for you in social settings, but generally other players can handle those and if there's a check you specialize in they could use your stats in a pinch - but when you're just dungeon crawling it's NBD to drive your character in combat or exploration). While I always have my wife to available to deal with any issues that may crop up with our child on game night, my players are fully aware that I'm willing to take over their character for a bit if they need to step away for an urgent matter.
At the end of the day it's important for everybody to remember _it's a game_, and we're there to have fun. The party member that regularly skips a session because they only seem to join when there's nothing better to do is a drag, but the vast majority of DM's and other players know that life is not so convenient that nothing will ever interrupt a scheduled session and aren't going to hold it against you.
One last suggestion: you can always do play-by-post. There's quite a few groups that operate this way, and it's a great way to get into the game without having to find 2-6 contiguous hours to play. The experience is most certainly "not the same", but that's the point.
Have you looked at how often you are actually interrupted for a meaningful amount of time during the time the children are, or should be, asleep? Try to get a sense of the actual likelihood and severity of the disruption, because these games can handle a player stepping away periodically for a few minutes.
I like your thought about data collection. I think the problem is more psychological. I cannot get deep into things if there’s a chance I’ll be interrupted. I’ve tried for years. The only video games I can enjoy are ones like Zelda Switch where small chunks are meaningfully fulfilling and I can pause at any point.
I was in a curling league last year and felt guilty and distracted every single time knowing my wife was on her own while I got to play.
Indeed this is very much a social and psychological problem with me and my family unit’s “free time” structure. But I look for external helping hands where I can, such as a “we have made this friendly to people who have to drop out”.
I used to love DOTA like games. God... when my first was born I was perpetually getting banned because I kept dropping out of games, screwing over 9 other people. :)
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.
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.
The reason I won't take a stab at this, as badly as I want to get into D&D, is that I have an unreliable schedule and can be pulled away at any moment (I have young kids). I won't even try because the possibility of letting others down is paralyzing.
I'm not sure if this is even something you can fix, but, there it is. And maybe there are ways to handle this gracefully without me letting the rest of the party down. In that case, maybe this is a communication/education problem.