M.P.
Ringworm is not bloody, they are not bumpy, they are small, red,sometimes crusty, sometimes clear circular wounds. They dont come and go, generally they stay till treated. They can be itchy but generally they are not. This is a FUNGUS. It needs to be treated by a doctor not a Chiropractor. This doesnt sound like what you kids have. Though its a good idea to have them get to the doctor soon.
Toxoplasmosis, but this does not manifest in any sort of lesion as others have said. It is a parasitic infection and gives off flu like symptoms and swollen lymph nodes.
cryptosporidiosis, giardiasis - Parasitic. Causing digestive issues and diarrhea.
Fleas, and worms. Flea Allergies can show up as itchy, lesions about the body.
Salmonellosis - Intestinal issues, diarrhea
Cat-scratch disease - Swollen Lymph nodes, fever, fatigue, general run down, icky flu like symptoms.
Leptospirosis - stomach ailments, fatigue, fever, headaches, Muscle pain, can turn into meningitis, Hepatitis, and other issues.
Lyme Disease - carried by the actual tick that might be on the animals. These have many manifestations and not all of them are the same.
So in a nut shell. Yes cats can give you ailments. That is why you should vet cats, and take them in for shots regularly. If ONE kitten has FIV, then the other has it by now. Its passed through litter boxes, and saliva. Some FIV cats do fine there entire lives with it. ITS HIGHLY contagious to other cats, so you dont want these cats to be roaming free. Some kittens dont live long with it. Depends how compromised the immune system is. Sounds like one of them is not doing well or wont do very well. So now for your daughters. What i think and suggest is just plain old, severe allergic reaction to CATS in general. Even though they are twins, one may not be allergic and one is. I would try keeping the cats away from the girls for one week. If they improve, well its the cats. Not the disease.
You? I would suggest Cat Scratch complicated by your MS