I know how you feel, i´ve been there too, my kid was "diagnosed" with allergies due to animals, and since i have dogs, it was like i CANT get rid of them, i LOVE my kid but i dont believe its the dogs, how come after almost two years he developed allergies to them and he plays with them but not that much, the dogs are bathed and parasite free so how could this be.......
besides children raised in an animal atmosphere develope more antibodies rather than allergies, so i stand for my dogs and bottom line the dogs where not the problem, and he just had a reaction due to weather shifts.

if mi kid were really allergic to my dogs i wouldnt get rid of them, and by that it doesnt mean i love my dogs more than my kid, i would just not let them get together for long periods and have a bit more precautions so my kid didnt get worse, i really hope your case ends well and you can be able to keep your cats........i really sympathize with you (my hubby has always said i love my dogs more than him (my hubby))