It depends on the age of your kids. For newborns, I wear my ‘street clothes’ to work and then change into ‘work clothes’ and change back when I leave. If you have a 5 year old, then F that!

Why is a Lyft dirty? I've ridden in many and I think they are probably cleaner than your minivan.

Word has gotten out in the nanny community. Good luck with your next hire. Honestly the level of control you seek over your nanny with zero understanding that they might need to use the phone (!) makes me think you might be happier staying home with your kids.
I don't mean that harshly. It's for your peace of mind too.

Goodness OP,

The change of clothes and no cellphone rule is very unreasonable.

You are absolutely the talk of the neighborhood, because the nannies are all talking to their employers about this.

Your husband is right to be mortified, because that's "crazy parent" behavior and you won't live it down until your kids go to college. People remember little tidbits like that.

This nanny is gone. Please don't propose changing clothes when someone has used a shared car or used public transport, it makes you look CRAZY. Please understand employees need breaks at work to call people, and they need to be stay in touch with dependents.

Wow.