Good luck! I came to tabletop role-playing after my kids were born, though the youngest was four by then. I’ll share my experience in case it is of interest.
Pretty much everybody in the games I GM are parents, mostly younger kids under 10 but a teenager too. Those with younger kids are pretty much in the same boat but parents of older kids remember how it was, so everyone tends to be very understanding about attempting to start at a certain time but bedtime is an aim and not always a perfect plan. there is also a bit more understanding when people are exhausted and and you may have to to reschedule or do something lightweight one evening.
When I started a game of blades in the dark we had scores that went on until past midnight the first few sessions but the group agreed that by 10:30 everybody was done so we now start at 8 and have around 15 to 30-minutes chat before doing a 2-hour session.
Interestingly dungeoncraft and other YouTube channels have recently come out saying that they have found shorter online sessions work better partly because it is not quite as immersive as playing face to face and there is an exhaustion with the screen interaction because people are on it all day.
in those two hours we can only really do a school or sometimes not even full score or downtime but normally not both. When I tried to push the pace the group actually pushed back that they wanted to go slightly slower and have time for the character moments in downtime and the free time scenes.
Every group of people is going to be different so I am just talking for my experience but the main takeaways are probably to allow a certain amount of time for decompression at the start of sessions that non parents may not need depending on how stressful their work is, and then absolutely cut to the action in scores because as you say that is one of the reasons for playing it this way but be aware that your crew may want to take their time at other points.
and one thing about the new normal that is absolutely awesome is that I get to play 3 games a week with my wife being in the party because we are not having to take turns leaving the kids at home while one of those drives to an in-person session. It has been a joy discovering how much we enjoy playing these games together. though it was slightly hilarious when we used to do dnd and share a character so that each session we had to come home until our partner what had happened so that they could go in the next time and carry on.
anyway whether that was useful or not I hope you have a great time. I picked blades in the dark as my first game to games master since my teens and and it has been pretty damn great. I hope you you find the same thing