I totally understand the mom guilt but definitely not warranted in this situation. You are paying the caregiver for her time and those are things you NEED to get done. Even if you were getting a massage, getting your nails, or any other self care you still deserve time to yourself!
If you’re paying your caregiver, then there’s no reason why they should be upset about you running errands during that time. I’m assuming your caregiver is a family member based on what you said, so I would either just not tell them you’re running errands if you’re set on not wanting another caregiver or I would hire someone else because it shouldn’t matter what you choose to do in that time. It’s hard getting errands done!
That's what you pay her for. If you're doing something important or its part of something important don't feel any guilt.