As a nanny I would not do:
cleaning the house
shirt ironing (while ds1 naps)
I would: picking up package
Though whose shirt would it be? DH should do his own. DS1 probably can't do his own, so nanny might well do that, though personally I don't do ironing - I'm no good at it and so I look for jobs where the parents are not fussy about their children wearing ironed clothes.
I see the children and the home as being my responsibility... so while "cleaning the house" is not done, sweeping the kitchen floor and running the vac around the lounge may well happen on occasion. If you need cleaner, get a cleaner (they tend to get paid more than nannies). If you just need someone to help keep on top of things... then a nanny may well do a bit of light cleaning if time permits. Children are unpredictable... children don't always nap in the day and certainly won't do as they get older.
I do/have done the following things:
Make bread (using the breadmaker)
Cook food for the children, bake cakes/biscuits etc.
Load/unload the dishwasher
Put washing in machine, hang to dry
Strip children's beds and wash their bedding
Call out emergency drain contractor when drains blocked
Figure out why central heating switches off when it's very cold outside (pipe insulation is great as a play sword)
Feeding chickens, chasing chickens, rat catching.
Basic plumbing - washing machine fittings for example.
So generally speaking, it's things that are related directly to the children in some way. Not things directly related to the parents.
If you do children's clothes washing and your washing together... then nanny could continue to do that. It's like the dishwasher, easier if everyone does it - so everyone fills it and when full it get's put on.