A.M.
I would say try using a petroleum jelly to keep her hands from being chapped. Also try doing mommie-and-daughter manicure days!!! Wash your hands together and soak them in a mild soapy water solution, whatever baby wash you use, and then dry them. File them down for her then let her do yours (or help her do yours). Next use the petroleum jelly as your nailpolish. Put it in a small travel container, so she won't know what it is to try to find it, and rub it on your hands together. Express to her that keeping her nails pretty will make them grow strong and that if she doesn't bite you and her will do this all the time.
I hope that may help a little.