No. A parent is exempt from the Household employee requirements (the so called "nanny tax")*. You don't give her anything but the $6000. If she wants to report it, she reports it as cash income. You should pay her by check, not cash, to create a paper trail.
*There is an exception to Grandparent exemption from the Nanny Tax. You should count wages to your parent if both of the following apply: (a) your child lives with you and is either under age 18 or has a physical or mental condition that requires the personal care of an adult for at least four continuous weeks in a calendar quarter, and (b) you are divorced and have not remarried, or you are a widow or widower, or you are married to and living with a person whose physical or mental condition prevents him or her from caring for your child for at least 4 continuous weeks in a calendar quarter. It that is your situation, then Grandma will need to file a tax return and pay approximately 14% social security and medicare tax on what you pay her. You should consider that in your decision making calculations.
