A.,
I went through this about 6 years ago. Cat and dog who loved to roll in the grass. I have a bunch of info somewhere on my computer, happy to send it to you.
*Without chemicals, nothing is instant, but it is worth the wait to avoid the health hazards.
Basics:
1) Crazy as it sounds - Vacuum. 2x a day, if not more, but definitely 2x. Get a cheap cat/dog flea collar, cut it into about 5-10 pieces, store the extras, and put one in the vacuum bag. (and rinse your hands, too, that stuff can be stinky :)
Doesn't have to be extensive, just has to happen.
2) wash the cat beds (if they have one) hot water.
3) wash your linens, hot water if you can for the fabric
(bleach isn't necessary - just the hot soapy water)
***If you catch one, hot soapy water. Nothing else will work, and he'll just crawl out to make more friends.
4) make sure your laundry isn't on the floor. Catch up with your wash if that is where it lands - need help with that - www.flylady.com - Mt. Washmore. :)
5) bathe the cats - simple soapy water, don't need flea bath with the kids, but you do need to bathe. Multiple cats that hate water, it's worth the trip to PetSmart, Petco or the groomer. Trick: fill the tub first, then have a cup and the soap and the towels handy. If you're lucky, they'll start to like the extra help with the upkeep. :D
The fleas will avoid the water - so short sleeves for you, and know that they will travel away from the water - which means they'll likely be crowding on the cat's head - this needs to be washed too!
6) For your lawn: especially if you have outdoor, or accidentally outdoor cats. Nematodes. Garden center. You have to do the application just right - dark night, not freezing weather, follow the directions on the package. These are helpful little critters you can't see (won't run into in the light of day) who prey on flea eggs (and a few other things in your lawn you'd like to get rid of). They have to be delivered to the lawn in the dark of night - we did it at 3 AM, but an hour after dark (not sunset :) will do it. Our lawn was free for 4-5 years (just starting to come back), much better than the 1-2 year guarantee on the package.
*** Worth it for flea=free picnicking.
If necessary, a trip to a boarding place that will put flea-meds on for you does wonders. The meds wear off after a month, if your kids are used to playing with the cats. Expensive, but will allow you a little time to get a handle on the vacuuming.
7) bathe the kids - it will help with the itchies. Don't have to soak a long time, and don't use soap more than once a day (unless, of course, they found the muddy puddle after all this rain! :)
**Remember: when you start getting overwhelmed with non-chemical remedies - remind yourself that it is for your babies! (and the cats and yourselves count too!) If you think the flea-bomb is easier, think again about all that powder going all over EVERYTHING - food, linens, floor, air, everything.
Good Luck maintaining your sanity, but you can do it!
M.