How much is one day nanny expected to do on the chores side?

Are you paid for all of the time you are there? Most jobs have a lunch break, but it is unpaid. I don't mean that I think that everything you have been asked to do is reasonable, but I would expect your lunch break to be unpaid if you don't have a child to care for during that time.

You should get a break, but you can still do some of those jobs too. Emptying the dishwasher, changing the beds and the batch cooking can be done while the children are there. You can do some ironing while the lo is at playgroup. You might need to explain to mum that some of the crafts/trips out might have to stop if she wants you at home cooking/changing beds. I would say general cleaning is beyond the remit of a nanny.

I would prob do dishwasher while child was eating breakfast and put a load of laundry in then. Then when childs at playgroup, I would hang laundry up/put it in tumble drier. I think you need to chat with your boss and say its not poss to do all that but maybe compromise. Tbh changing beds shouldn't take too long and maybe you could cook a meal and freeze it. I think I would say that the dishwasher and changing childs bed is fine but you can't do both ironing and batch cooking so it might be that you do one or the other.
I have a friend who has similar issue. She used to do 4 full days and then it went to 2 half days ie 2-7. The family still expected her to get everything done but as she doesn't start til the afternoon and needs to cook dinner for the boys, pick them up from school and do homework/activities etc she doesn't have much time. So she picks up laundry and puts it in machine but her boss has to finish it off from whatever stage its at when my friend finishes. She now only does one afternoon and she chatted to them and she cooks the boys dinner but does enough so she can freeze a batch and she only does laundry if its something that needs doing for the next day. she will do small amount of ironing(the first hour is childfree and she quite often cooks when the boys do homework)

I feel the key thing to remember is that you are there to make the parents life easier, not just care for the children.

Finding the right balance between care and housework can be tricky. Helps if everyone involved is realistic.

I would make beds possibly change the bedding on abed. I would load/unload the dishwasher, put a laundry load on. I might set the breadmaker going. Might vac the floor in heavy use areas.
I would no do ironing (but that may just be due to me being rubbish at it).

2 hours is not that much time though quite a bit can be done and some things can be done pre/post pre-school.

Nannies don't get a break, I am very lucky that in my job I do get a break some days but that is not usually the situation in nannying.

Are you at home for 2 hours, or is that the total time the child is at playgroup?

If you are at home for 2 hours between school runs then I would say have a sit down break for half an hour, and then you could alternate say change the beds every week, and then either iron or batch cook alternate weeks. I don't think you should be doing general cleaning though.

It would only take 10 minutes to unload the dishwasher while children eat breakfast though, and surely you need to be able to refill it during the day?

Think you need to sit down and chat to mum

Not possible for you to do everything and not should she expect it all as you are there one day

It's fine to do one thing off that list so either batch cook or do some ironing or change beds and put washing on etc

Being a part time nanny 3days I have always said to employers that I am happy to do nursery tasks but they need to rem that I am not there full time so for example I can put washing on change beds and batch cook but come Thursday they will also have to do washing etc

Tbh usually a one day nanny wouldn't do what you are doing but think as you have started at 2 days and gone down to one the mum hasn't reliesed you will have less time