I'm fairly certain that all the OP asked was what people would do if they had some alone time at the world, because they'd brought a nanny. People's unsolicited and rather snarky comments on her personal life, who her nanny is, or how much she's paid are irrelevant and superfluous. Jealous much?
Regarding what I'd do if I had a nanny along, I'd probably spend a lot of time doing some deeper exploration of the World Showcase in Epcot, and also Disney Springs (to a lesser degree). I think I'd spend time in areas that we usually skip or rush through like Hall of Presidents, Main Street exhibits and unique shops, etc. One PP said they start out the morning with the kids, split off during the day, then get back together in the evenings to finish off the touring. I like that agenda. And my unsolicited opinion is: Good for you, OP, for taking some initiative to book a trip that is incredibly special for the children, but being wise enough to make it a special time for you and your significant other as well.