I only have two kids (luckily), but I work out 6 days a week.
I've got a set of gym equipment I keep at the end of my garden (proper gym equipment is really robust).
I'm up at 5am to do a either 10KM or an hour on a spinning bike plus some resistance work and after the kids go to bed, I do a small amount of kettlebell work.
The principle is... before they wake-up and after they go to bed, and also to get your own kit.. Its relatively cheap also.