I'm watching with interest as we're in the same position - two full-time jobs, two kids (8 and 10), a teenager who is currently working full time and a dog.
There are so many brilliant ideas on here, but sadly, all of them take an injection of cash. Our business has been hit badly by Covid and we've had to slash our income by about 50% while also having to work all hours to rebuild and recover.
For what it's worth, here's our approach:
Saturday - check diary for the week ahead (do we need birthday cards/Red Nose Day stuff, etc), sort a meal plan and food shop for the week, clean and tidy
Sunday - sort laundry including two sets of school uniform for the week, plan ahead for the week for work
Monday 6am - plan my diary for the week ahead blocking out my personal time for kids/school runs/appointments/dog walks/20-min Peloton sessions, then add specific work tasks around those. I do personal time first as otherwise it just wouldn't feature.
Weekdays - I get up early and start work in the quiet, usually around 6am. I sort the kids' breakfast then DH chivvies them along, dropping them off on his way to the office. I work from home to embrace the silence.
I collect the kids at 3pm, bring them home and then carry on working around them before taking a break to sort their dinner (while it's cooking, I make the packed lunches for the next day), shower or bath, reading, etc, and check if uniform is clean or put out fresh.
DH gets home around 7.30-8.30, he sorts dinner (stir fry, pasta, Charlie Bingham-style ready meals or sometimes just soup and toast if we're too knackered to eat) and tends to listen to the kids reading before tucking them in, and I then sit and pick up on emails and admin from the sofa. This feels absurdly luxurious after a day mainly spent at the kitchen table.
I tend to crash out before 10 so I can get a decent amount of sleep before getting up before 6. I am NOT a morning person and it's a struggle every day, but I seem to be quite productive at that time of the morning so it's working.
I don't feel I get a lot of quality time with the kids but they're of an age where they get home and want to disappear off to another room to talk with their friends on FaceTime, watch TV or read, but they know I'm close by. As the weather improves, I'll combine collecting them with a dog walk in a local park which will mean they spend more time with me and less time on a screen.
Their sports activity twice a week starts again soon which will make things a little trickier, but I can combine that with a dog walk and a podcast so it's not a hardship (unless it's raining, then it's miserable).
There's no doubt this is tough, but for now, we're just digging deep until things improve - which we firmly believe they will, the green shoots are already there. I miss having a cleaner each week, and I miss regular takeaways and the luxury of being able to solve things with money, but for now, it's OK.