When I was a full time nanny (8 years with the same family), they did 6-8 weeks of vacation a year. If they chose to take time off, and didn't need me (I did travel a few times with them over those years), I got paid.
How would it be fair for the nanny to lose that much pay because YOU decided to go on vacation? Now suddenly she is told, "oh we are going out of town at the end of the month, so no pay for you for the week". To her that probably means part of her rent, car payment or insurance! I loved my nanny job, but every penny mattered.
When I was a nanny, they did have a dog, and often, if they left town as a family, I was asked if I wanted the dog duties, which meant staying at their house. It also meant MORE money for me. They paid me what the kennel would cost them, per day, on top of my paycheck. My then boyfriend, eventually hubby, and I lived in tiny apartments, so staying in their nice house, with a laundry room right there, a hot tub outside, parking in a garage in winter, etc was like a vacation for us!
It was a farther drive for him to work, but I did extra stuff (cleaning out kids stuff, sorting seasonal things, walking the dog, getting groceries before their return date as per their list, etc). Sometimes they left me a list, other times they did not! One time we even had my whole family of 25 people there for Christmas, at their urging, while they were in another state with their family.
I was off contract really the last 7 years I worked for them. We sort of winged things and it was mutually beneficial. I quit when my own child was 3 years old, their youngest was starting first grade, and it was time for a change for all of us. It was hard on all of us. We never had an adversarial relationship. They recently attended my daughters graduation party. We still communicate!
The relationship is what you make it.
Best wishes.