I would hope that any nanny I hired would be able to show good judgement. In this case, I think what you did showed logic and reasoning. I don't need to micromanage, although I expect that my rules will be followed. The MB is usually not available during the day, so you made a judgement call that you believed was in the best interest of the entire family. This was not a big deal, since, as you stated, the kid missed nap and playtime. Had you chosen to just not send him to school for the day, that would be different.

But, in this situation, I probably would have expected a quick text letting me know that you had decided to do this. I certainly wouldn't be mad if you didn't do that, but I would probably just ask you to keep me in the loop next time, since I am the mom.

OP, I'm just wanting to understand a little more. Could you explain...

Do you normally pick the child up from daycare? You just picked him up a bit earlier than usual? you have a car seat and permission to drive him?

You were already at work, right? You were with the child's sibling at a play date? So it's not like you were sitting at home waiting to start work and thought "hey, I think I'm going to pick the child up early today, I feel like starting work now!"

It sounds like your intentions were good. You were already out with the other child and since you thought the weather was going to be very bad you decided to pick the other child up, instead of going home and then back out in bad weather. If your MB is mad, it's her thing. Maybe you should have called or maybe you shouldn't have picked the child up but honestly, if she's super upset about it there's probably something else going on with her. Try not to worry about it.