Grrrr....
I had a similar problem. We adopted Patience and Sissy from a litter found in my mother-in-law's shed. I didn't know they had fleas when we got them (maybe seven weeks old), or we probably wouldn't have. I'm so glad I did, though.
Anyway, we tried EVERYTHING. Well, almost. Dawn dish soap is supposed to work well, but you have to use a lot of it. We tried this, but I don't think we used enough because it didn't work. You will have to be very careful doing that with kittens this young because they might get too cold. Baby powder is supposed to help, but it didn't for us. I ended up finding some flea spray at my local Pets R Us that can be used on nursing kittens and mothers, but for the life of me I can't remember what it was called! So you might want to call around at local pet stores or your vet's office to see if they have anything that can be used on kittens that young and nursing mothers. Most treatments can only be used on kittens older than 12 weeks. Using a flea (or lice) comb helps, but make sure you fully submerge the fleas in soapy water or they will jump right back onto your cat!
The biggest problem you are going to have is passing the fleas from mother to kittens over and over. My suggestion would be to take all the cats outside of the house for a while so that you can flea fog it. I used many types of foggers and sprays to mostly no avail because I couldn't keep the fleas off Sissy and Patience. I found the best success in (believe it or not) shaking IODIZED SALT on my carpets! I've also heard of using borax and sevendust, but it's toxic to cats so I wouldn't use that.
After my cats got old enough, we started using Frontline, but honestly, we still have the occasional flea. We've been battling this problem for almost six months now...but it has much improved!
Good luck a million times over.

whenever we got a new young kitty, my mom and I would give her a bath, and comb her while still wet. We used to pop big fat ones, and they were so easy to spot with the wet fur. After that we would just flea comb them every day...eventually the fleas just disappeared. It helped not having a carpet...but then again we lives in a hot environment. What the vet told us one time, is that cats get fleas when there's a lot of dogs around in the neighborhood. I have no idea if this is true, but our fleas dissapeared even though there were dogs in the other apartments. They're fun to pop, though! (i know, eww but fun)

Yeah as gross as it is, I get a vengeful satisfaction out of popping the fleas. You won't take my cat's blood and get away with it damn you!!

I would recommend Frontline Plus for fleas, it works better than anything else, especially when you have multiple cats, and it's the only thing that kills flea eggs and larvae. You shoul also wash the pets bedding (and yours if they sleep in your bed), and vacuum every day for the first few days after application.

As for the wee ones, I can't remember if you can give the mother flea medication or not, but I know the babies can't have it yet. And yes, you have to wash and comb the babies until they are a little older and can have their own medication. I would recommend, if you have the money, Paul Mitchell's Pet Tea Tree Oil Shampoo, it is gentle and the tea treee oil helps with fleas and skin irritation. Also keep an eye out for worms because the babies are very susceptible to them if they have fleas, and often the mom will get them because she cleans them so religiously. I know you can give the mom wormer while she's nursing and that will help the babies as well.