You will be credited the price you paid for your tickets, toward your upgrade to an AP. So if you paid $214 for your ticket, you get $214 credit toward your AP. If you paid $254 for your ticket, you get $254 toward your AP. So in short, it doesn't matter how much someone pays to get in--it's going to cost the same amount out-of-pocket when they upgrade to an AP.
Basically, you can't use your GAD to upgrade a partly-used park hopper (even if you used it for just that day).
But you CAN upgrade your GAD to an AP or a hopper.
In other words, if you go into the park then you can pay the price difference between your GAD voucher and an AP (skipping the park-hopper entirely). OR, you can upgrade your GAD voucher to a park hopper (and then later upgrade that park hopper to an AP, if you like). This is the way to go if you want Magic Morning or have some AP blockout dates during your trip.
Provided you're visiting after September 30 (when the current deep discount expires), I don't think there's any good way to handle your child's ticket. If you're upgrading to Deluxe APs, that's probably the way to go. (If there's a good chance you'll be visiting
Disneyland again before a year's up then getting an AP is a great deal regardless.)
6-day plus 2-day = $184 + $139 = $315
5-day plus 3-day = $179 + $154 = $333
4-day plus 4-day = $169 + $169 = $338
Have a great trip!