The last resort is to put a 3 yr old down, over what I am assuming are allergies? Are these skin infections or what? Find a qualified dermatologist if there are any in your area and start there. Surely wherever you are there are Specialists?
Good luck, I am in shock they want to put a 3 yr old to sleep
Please give us more information on her ailments. and the things you have tried so far. Have you done an allergy test on her? Which kind?