@ClaraThree
I haven’t read all replies on here. I’m a nanny.
Yes I would expect your nanny to go out each day. Morning to park or groups , nap in afternoon and then possibly walk , activity again but all should be child centred . Not to shops . Although occasional trip to garden centre to see plants , fish etc fine.
Your nanny should be doing activities at home eg messy play, crafts , playing with toys , reading books.
Does your nanny have a childcare qualification?
This ^
@Strawberryjam45
Your DS could benefit from a little more time at home to explore his interests in an unstructured safe environment eg crafting, painting, building blocks, imagination play, baking, messy play, water play. You should ask the nanny to schedule this in a few time a week.
Visiting the shops should be occasional and purposeful eg fine to pop in to pick up nappies or look at the Christmas lights, but there are better, more appropriate places to take a toddler for entertainment and education.
Nanny taking your DS to her home shouldn’t be happening. She’s not a childminder so her home is not inspected as child safe. Do you know who else is in the house? Presumably she isn’t insured to carry out her job there either so it puts her in a tricky position if DS has an accident.
Nanny taking DS out with her DD is problematic. You are blurring the boundaries of your relationship as her employer. Her DD is not your employee. She is an untrained, uninsured child. She is not contracted to be responsible for your DS. If it keeps your nanny happy, you may choose to allow her to bring her DD along on days out. You should clarify the boundaries and lines of responsibility in writing. Your DS should never ever be left in the care of the teenage DD.
Also if this is your long term nanny, you should insist that classes are near where you live so as he gets older, DS can make some local friends.