Show them this link:
http://www.irs.gov/publications/p926/ar02.html#en_US_2012_publink100086722
It's from the IRS publication 926 the household employer's tax guide. It will show them that a nanny is classified as a household employee not an independent contractor and her taxes should be treated as such. They are just trying to get out of paying their share of the taxes, and they can't really argue with an IRS publication.