I do the main food shopping, but my AP will run out and grab milk, OJ, etc...if we need something. If you have an AP with any common sense, she will do this as a member of your family.
Of course, as do most APs. However, the OP seems to think that the main grocery shopping can fly. APs are not a less expensive version of a professional nanny who is going to care for the infant and while the infant naps, do the household laundry, clean up, start dinner, and when the baby wakes up, do the household grocery shopping. And too many HF enter the program with a false understanding of what APs can do.