I had a similar issue. Since I receive my AT&T bills via email, I never changed my address with them when I moved earlier this year.
When I went to check out on the apple.com page, I noticed it had my old address, but the option to change it was grayed out.
First I tried to change my address on the apple.com Account Settings page. While it allowed me to change the address, when I checked out again, I noticed it still had my prior address.
Next I went to the att.com page and changed my address with them. Then went back to the apple.com page and reordering the new iPhone. New address was now reflected.
Apparently Apple's ship to address is locked using the mailing address in the carriers' system.
You could ask your dad to either order the phone for you via the AT&T page (maybe it gives you the option to change the ship to address) or have him change to your mailing address on the att.com site, allow you to place your order, and then switch it back so he continues to get his bills.
Real pain, but I guess there was a lot of fraud issues with the first iPhone releases and this is how Apple and the carriers agreed to work it out.