Kids laundry, keeping their bedrooms tidy ... and cooking for the kids are the basics.
As a "family member" : dishwasher, cleaning up after dinner, taking the trash out ...
Meaning that sometimes the parents do it as well, it's not a one way street ...
The AP shouldn't cook for the whole family unless she wants to. She's not there to cater to everybody. But asking her to cook one easy dinner a week sounds reasonable.
The whole food shopping can't be done solely by the AP. But she can go to the supermarket and grab butter, bread or whatever items are missing.
The master word here is to be reasonable on all aspects.
I'm sure you can ask for more but you don't have to force it, just ask if she's ok and pay a little extra, I'm sure the AP will agree to do it.
I used to be an AP and my family asked me if I'd agree to do some extra cleaning tasks during the baby's nap, they gave me some $, it wasn't much but it paid my monthly subway pass and it meant a lot to me

Everybody was happy.