remote control doggie door
This seems to be divided into two problems. First, the remote control and secondly, the electromechanical control of the door.
With the remote control portion, there are some off the shelf stuff that can be used. The cheapest solution is the X10 home automation stuff. Go to
www.x10.com and search for home automation. There you will find wireless remotes and boxes that can control an electric outlet. Into this controlled electric outlet you would plug the soleniod that controls the door. This equipment is also available on Ebay, some Radio Shacks, and many resellers. In addition to controlling electric outlets, they make modules that control a switch or a relay, if that is required.
I have seen these remotes work across 300 feet. If it is clear line of sight, then it could possibly go 500 or more feet. People have tweaked the receiving antenna also to increase the distance.
Higher up the price curve are other companies making home automation equipment. Do an Internet search and you will find others. If the 500 foot distance is serviced from a common electrical panel, you could also do powerline communication.
For the mechanical portion, you may want to consider a magnetic lock.