To do this, first off use WEP on your wireless network to start with. Second yes use SSH using certificate authentication so you don't have to worry about enterting passwords. In my view what would have to happen for this is:
Userland app on Empeg pings for your home machine every second on the wireless interface. Once it pings good it should connect using SSH and once it does it runs a script to open the garage door. Seems simple enough but the details (like how quickly will your wireless interface will "see" your home network when it's within range) will be enough to drive you mad. Good luck.