Um, why not just install an email client and check all your email at once (I believe there are numerous, free email apps out there, or Outlook if you're stupiddesperate)? Google is one of the few email providers that allows IMAP. Also, doesn't Google let you check a different email address through GMail? Couldn't you have set your primary account to also check your secondary account (no, I'm not talking about forwarding)? I mean, I know I can tell Yahoo to check my Gmail (but only with POP, which sucks).
Here's another trick. Use a browser with Private Tabs (Porn Mode). Since the tabs don't interact with each other, you could log in on separate tabs, links still work, and better yet, when you close your browser, it clears the memory and doesn't leave you logged-in (also wipes tracking cookies and other crap).
Seems to me, the need to login multiple times is simply a work around to other, better tools that already existed.