I agree, if she has been outside at all since having her kittens, have her spayed NOW! If she has been inside only, then you can wean the kittens first, and let her milk dry up for a week before spaying.
If she has been outside at all, you don't have the luxury of waiting. Vets spay barn cats and ferals all the time...so it can be done. If the first vet you call says no, call another and another. Maybe even call a rescue, so they can recommend their vet to you.
Best of luck. Thanks for ending the cycle of endless reproducing for this kitty!