Not working while nanny is at my house?

I work from home 100% of the time. We have our nanny in our house from 8:30-5:30 and pay her overtime for all hours after 40/week.

Here’s my question. I always feel so weird not working while she’s in my house caring for my kids. By not working, I mean specifically exercising or running errands. My job is somewhat flexible which allows me to exercise during the day for 30-60 mins or run an errand here or there. But I feel so uncomfortable doing it! I feel like if she’s in my house I should be working or relieving her of my kids. We have a home gym that she has full access to and she uses when the kids are napping and I always offer to pick stuff up from the store for her.

Nannies, do you get annoyed if the mom or dad works out, grocery shops, etc. while you’re there?

Editing to add: we let her go home early at least once a week (but still pay full hours) and she gets lots of “extra” time off because we don’t have her come in when both my husband and I are off work. Like we’ve been off work the last two weeks so she got bonus time off, all paid in full.