If you want to get around a realm down, there's only one way to do it.
When you get a Realm Down, Blizzard Blocks your IP Address from logging into the account. If you wanted to login to your account from another computer you could, thus, its your IP.
If you want to change it, go to this site.
Whatismyip.com
Click the link that says Change my IP.... If you follow those easy steps, your IP will be changed, and you'll be able to login.
Good luck.