You are NOT required to pay nanny taxes for a household employee who is your (or your spouse's) parent. A household employee, by definition, is one that works in your home, not theirs. Even though you are exempt, you are still allowed to issue them a W-2 or even a 1099-Misc. It's just not mandatory. A 1099-Misc will subject her to self employment tax.
You do not "have to" issue a W-2 in order to use your FSA, but it could be helpful. You do need to provide her SS# on your form 2441. So, it would be a good idea for her to report the income, on a tax return, even if she is not otherwise required to file.
One of my previous replies, above, describes how she enters her income, in TurboTax, without a W-2 or 1099.
