When I was a nanny there were 7 children in the family ranging in ages from 18 months up to 7th or 8th grade. The mom's boss had one child and she paid me separately for his care, our wages were set up between us. They were comparable but she just paid me by the day whether he was there the full day or not. That worked out for me nicely since I could count on a certain dollar amount each week. And yes, I was responsible for paying my own taxes and SS. I did file the taxes on my income each and every year I worked for these 2 families.
For the family with all the kids I was paid by the hour per child. If I had one I got paid for that one child, if it was a day out of school for mom I got paid for the kids that were there under a certain age. If I was not there those older kids would be old enough to stay home alone so they did not need supervision.
I got paid by the hour separately on top of the wages for the child care to cook, clean, do laundry, mop, take out the trash, sort clothes in rooms or clean the kids spaces that were not a mess of my making.
So it was NOT my job to be their housekeeper. I did clean up after myself, that was part of my job. If we made a mess fingerprinting with pudding I was to clean up the pudding thrown on the floor, the chairs, the table, etc...it was our mess and therefore part of my duties.
Once the one dad got home at 3:30, the kids got home on a normal day about 3:15, I was "off duty" from watching the kids and was paid by the hour to cook dinner and do any other chores she wanted me to do extra.