I'd find it a bit weird to log into a site and end up on a different site, but that's your choice of course.

One way around is to do it as you do it now, but encrypt the password with something like Crypt::CBC. You just need to a common, secret key or passphrase on all three servers.

This doesn't scale to sites that don't trust each other, in which case you need something more complicated, like for example OpenID.