We give our AP a Visa bank car and drop money on it for gas, groceries and incidentals. Sometimes we ask her to grab the family milk, bread, fruit or whatever from the store. Super easy and I don't have to worry about receipts and can see the spending. Never had an AP abuse it. However we also pay for APs personal gas and don't nit pick avocados and mangos. Averages an extra $50/wk. Our AP also doesn't drive a ton because she like to drink and always ubers or has a DD.

$50 + stocked kitchrn

If you go away on vacation and AP stays at home, how much grocery money do you leave them, or do you just buy everything up front and leave the kitchen stocked?

Same experience. I always ask what the au pair wants from the grocery store before I go. Lists get longer and more expensive as the year goes on, especially as they have more friends and all want to cook/eat lunch together. They over estimate what they want/can eat and if it is still there by Friday and perishable I will often cook it before it goes bad. I just can’t watch expensive food go to waste.