2 sign ins for same webpage

[JirafaBo]

I run two accounts for the same webpage. I want to create a shortcut to both accounts for the same page. I tried to make a bookmark for the normal log in site with account A, and then logged out, and used the logout webpage for account B. For some reason it still keeps bringing up account A no matter what page of the site I bring up to log in.

My friend did this for the same site, on his Android Touch and it works for him. I even cleared out all caches/passwords and tried to start from scratch and still cant get it to work. Any ideas?