Welcome to the forum, Cecilia!

How terrible that while in a pet shop, the owners didn't get the kitten treated for the worms (or was it in a very, very poor town?) Bless you for adopting the kitten and getting her vet care. Do you have an idea how many weeks old the kitten is?
Only afterwards did I read the site where it said not to integrate a kitten with an adult cat.
It's not that one would never try to integrate a kitten with an adult cat. It is just that most adult cats don't like little kittens so most adult cats don't act like playmates or "mothers" to little kittens. Little kittens tend to be annoying to adult cats. So if one decides to get a young kitten, one needs to realize that the adult cat isn't going to be happy about it for a while- many months, until the kitten grows into a cat and out of the annoying always wanting to play stage. If one is getting a new cat on purpose wanting it to be a playmate for an adult cat, that is where the caution about not getting a young kitten comes in.
Certainly, if one finds a kitten in need of help, one would take it in, even if the adult cat or cats won't be happy at first. You just keep them separate a lot and for a long time, understanding that it might take months for the adult cat and kitten to at least "live and let live".
Do read my article about integrating kittens with cats at
http://wvcats.com/integrating_kittens_with_cats.htm. Even if you read it, read it again as you move along in the introduction steps.
Here is my problem, the last few times I had the little kitten in the cage the big cat walked up to the cage, pressed her face against the cage, made those deep throat noises, spat and tried to claw at the kitten. Why is this getting worse?
It seems for your adult cat, she needs a
lot more time to accept the kitten even being in a cage.
I would stop the cage viewings for 2 weeks, and just do the room swapping. I would maybe once a day for 3 or 4 minutes put the kitten in a carrier, and sit with the carrier on my lap, to allow the kitten to see the adult cat, but not be possible for the adult cat to get near the carrier.
Keep in mind that it can take 6 or 7 months for the cats to accept each other. So take each step very slowly. If the adult cat growls, then back up for a few days.