This is my scenario and strategy, albeit, our circumstances are different, but perhaps you can pick up a tip or two.
3 kids - 9, 6 and 3 years old. Both me and the wife work full time. The 2 older ones are at school, 3 year old is in creche.
We have a nanny, and I will rather give up half our other luxuries than get rid of her, this is how we claw back I would say at least 50% of our time i.e. washing clothes, ironing, cleaning house, preparing food, babysitting etc. I don't have time for all of that, and prefer to spend all my spare time with my family and on myself.
I wake up at 04:00 to run, by 05:00 I am back, by 06:00 the kids are up and getting ready for school - this is my "me" time in the morning, I get to exercise, shower and have coffee before the madness begins. Trick with this is you have to be in bed early-ish. Then I always do the school drop off giving my wife 30min to do some exercise and then shoot off to work.
Me and my wife tag-team a lot in order to give ourselves more "me" time e.g. I run on the Saturdays, she looks after the kids. Later in the day she goes out with her girlfriends, I keep the kids busy - otherwise you never find alone time.
As a couple, we fortunately have family around, so leverage off that for weekends alone away etc. And then the nanny steps in during the week for date-nights etc.
In terms of involving the kids, absolutely, even if they are babies, pop-them in their high-rise chair, jolly-jumper, whatever, and place them close to where you are doing your chores, they get entertained and you get the job done.
In closing, as they get older, it gets easier - I would say around 3 years then you are better off, and then around 5-6 years old you slowly get out of the woods because then they are fairly self-sufficient.
PS: Work-life balance is critical, don't sell your personal time to your company, you will never get it back, and if you die, they will forget about you in 1 week.