What would you do /say in this position?

I would tell them this is my rate for being a nanny. And this is my rate for being a nanny/housekeeper. (If you are willing to do housekeeping)

I think you have kinda answered your own question in that you know what is right and what's wrong... you know that you need downtime if you are going to be able to give your best to the child... if you are tired and overworked you are not going to be the best nanny you can be.. You could explain that to the parents? or you could just explain that a housekeeper is a housekeeper, a nanny is there for the child.. 

It was always my understanding that, if a person is getting hourly pay and is "on the clock," they should be doing something to earn the pay. When I was a teen and doing babysitting, I cleaned the house after the child went to bed. I'd wash dishes, scrub the kitchen, do the floors, whatever, simply because I was getting paid to be there. When did daycare, it was in my home, so that wasn't an issue. When I hired help to take care of my disabled mom (I was lucky enough to be able to pay a caregiver for a few hours each Sunday, so I could sleep or work uninterrupted), we set clear expectations in our contract. She got a set pay per day, rather than hourly, and I asked her to try to take a real break (30 minutes or whatever) when my mom was taking a nap. I also told her to grab two 15-minute breaks whenever it fit into the schedule. Those are the standard breaks required of companies, so I went with it because it seemed reasonable. She structured her own day around her needs and my mom's and I considered providing companionship working, even if they were just sitting there watching TV. Aside from the breaks, I asked her to stay busy when she wasn't with my mom, and she did. Boy did she ever. My house was never as clean as it was than when that woman was there as a caregiver. I never asked her to do anything specifically- just to stay busy when she wasn't on a break.

From a caregiver/ nanny standpoint, I think M2C gave good advice, but I also think you should negotiate your contract and set expectations from the beginning. You should set your pay according to what you're willing to do and make sure the parents understand what you'll be doing and when. Most parents won't ever manage or hire someone aside from a caregiver/ babysitter, so they won't understand the nuances. You'll need to take the lead.

Your question also reminds me of when I worked in a dental office. I was a dental assistant and went to school for it. We did lots of patient care activities- assisting the dentist, taking x-rays, getting patients ready, some minor treatments, etc. And, then we had side work, like cleaning and sterilizing instruments. I'll never forget the day I was cleaning up after a long day of patients. I had a new dental assistant shadowing me and was going room to room collecting the trash bags to take out. I asked her to grab one while I did the other and she refused. "I didn't go to school to take out trash," she said. She didn't work at that office for very long. We all do crap we don't like to do alongside our primary jobs. It's a fact of life. Adulting. It would be very unwise to refuse to do side work in any job, but you should be compensated fairly for it.

I am probably not going to be much help; but I can tell you as a parent, I'm on your side here.  If you are taking care of my young toddler, I expect you to clean the area around the diaper, but not to extend your work into the master bathroom.

If I trust you to be vigilant and care from my child, I am willing to pay you for that, rather than make you a utility employee, serving wherever I say I need you and doing whatever I need done.

On the other hand, if you are willing to do a few things around the house, I would be willing to pay you ad hoc for such work.

That part about "doing things not expected of a nanny" sounds a bit broad - like they might be expecting you to rack the leafs in the yard or clean the gutters. It's been a long time since I had to look after a toddler but if I recall they might be napping one moment then up and getting into mischief or danger the next moment. So I figure as a Nanny you have to always have the child in sight and ear shot. Ideally as a Nanny well the child naps you should be making a sock puppet for a fun activity when the kid awakens or preparing nutritious snacks or lunches. Cheers!

I worked as an au pair once, supposed to be helping out with two children and going to language school for half of the day.  I was there a week and the parents took off for ten days, when they wanted me to clean carpets I found another job fast.  I was too young to insist that certain things were not what I was being paid for so I would strongly urge you to have a conversation with the parents as to exactly what you're prepared to do.
Taking care of a toddler is in itself a full time job, they have more energy than an entire football team so you should be prepared to do things toddler related, perhaps doing the baby laundry but not cleaning the house that's something they should pay a housekeeper to do or pay you a lot more than a nanny's pay.
Look at it another way, how much would it cost them to put the toddler in daycare?  That should be your guide as to how much you should be making for child care alone.

i think you should do whatever the parent wants you to do if youre working for them