It sounds like she has mastitis which is an infection of the mammary glands. She will need antibiotics to treat this problem. She can make the kittens sick from nursing on an infected nipple, so trying to get the kittens away and get the infection treated is somewhat important. Your local humane society may be able to provide you with humane traps that you can catch her and get her and the kittens into the vet for treatment. The kittens need vaccinations as well as spaying and neutering. Most vets will do this on feral kittens as young as 6 weeks because it can be so difficult to catch them. Probably the only way to turn her and the kittens around is to resign yourself to making them indoor only pets. You will need to work with them in order to gain trust. After having them vetted, confining them to a small room with food, water and litter and possibly a large cat tree will help you win their trust. Purchase a laser pointer or some kitty teasers from the pet store or on ebay.com and play with them from a distance at first. It will take time to win them over, but with patience, especially since the kittens are so young, you should be able to do this. You may want to talk with the vet about the treatment for mastitis as she is probably not going to be cooperative with you about taking oral medication. Your vet may be willing to treat and board her until the infection is cleared up since you are willing to give her a good home. Good luck with your new family and bless you for taking this brood in....you are wonderful!
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Lori McLaughlin
Your veterinarian should ALWAYS be consulted first and foremost when your pet's welfare is at stake.