Grandmother paying for child care for out of state grandchildren

Hello,

 

I live in Massachusetts and I am about to start paying for my Grandchild's nanny. My grandchild lives in Illinois. Since I am paying the wages, am I considered the Household Employer even though I do not head the household where he is cared for. I assume I should pay SS tax, medicare tax, Il state tax and any required federal or state unemployment insurance. Am I missing something here?

Thanks