I think that you will be asked for your proof of residency when you get the pictures taken. Now your kids, that might be a grey area, b/c they could live with your grandparents, and kids don't generally have ID.
But also please note that the two southern CA APs have very limited dates, so it's not just a discount on a Deluxe or Premium AP, but a much more limited one (er, two) for residents.