A clean home has always been a priority for me.
Once it’s in a good state, maintenance is really not that hard (I also have 3 kids).
Kids can help plenty! Get them into the habit of tidying their toys, putting their laundry in the wash basket and making their beds, every day! We used to put all toys away between each transition, ie before we go out, before a meal before bed.
Wash up after every meal. Do a load of washing every day (and put it away as soon as it’s dry - kids can help with this too).
Hoover round soon as the kids are in bed.
Once a week do bathrooms, hoover upstairs, dust. Do these on different days so you’re looking at 30 mins daily jobs and 30 mins of weekly jobs.
Can you ship the kids off for the day and have a friend or partner help you blitz it, so you’re at the point of maintenance?
When I’ve worked full time I’ve had a cleaner, but always did the daily jobs so it never gets into a real state.