Everyone has given good advice. I have trapped, spayed/neutered 2 ferals who have both turned out to be cuddly, sweet--and grateful house kitties!
I would advise you to borrow a humane trap from the shelter, a vet, a rescue group, put tuna or something equally yummy in it, and trap her ASAP BEFORE she has the babies.
You then have 2 choices: 1) take her to be spayed (and aborted at the same time--many rescue people and vets think that if babies haven't been born, they shouldn't be born because of the terrible overpopulation of cats) or
2) let her have the kittens indoors, tame them and find them homes. The second is the most difficult and expensive. It costs more in the long to raise kittens than to spay their mother. Do go to the low-cost spay/neuter site you've been given; also, call local vets and find out if they would give you any kind of 'deal' for spaying a feral kitty that you are trying to help.
Now, she NEEDS to be indoors. Can you keep her in one room, away from your 5-yr. old and other people, where only you visit? Or, can you get (borrow?) a cat playpen to keep her in while you work to tame her? Maybe the pen could even be in the garage if you don't have a place in the house where the kitty is 'safe' from too much goings-on. With my ferals, I trapped, neutered, vaccinated, etc. and then brought them home to a pen in the room where my computer is located. That way they would get used to people in the room with them while still feeling safe in their enclosure. I also talked to them, and the first one I even read aloud to. Eventually they came around--a couple of months in both cases. Both of mine were 2-3 years old when I trapped them.
The most important thing is to get her BEFORE her babies are born if at all possible. If she keeps having babies somewhere they, too, become feral. And on it goes...
You are to be commended for wanting to help this cat. THANK YOU so much!! And best of luck to you and the kitty.
Norma
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The 9 Wiscats: Every life should have 9 cats!
Monsieur Gervais le Blanc (married to the divine Shelby)
Gentilhomme Beau (meowrried to Meadow, da luff ob hims life)
Andre-Guillaume (luffs Maria Noblecat)
Henri le Chanceux (haff begun dating Miss Bayli Minnesnowta)
Frere Simba (married to the beautiful Sassy)
Madame Minette (Nortee's beluffed, mama of Poucette))
Annie-Claire (TEEN daughter of Poucette and Rexy)
Poucette-Noelle (luffing wife of Rexy, mama to Annie and Antares)
The Excellent Lady Sophie-Marie (widow of Spunky StLouie)
~~and varying numbers of foster kitties coming and going~~