I need to redirect authenticated users from Wordpress site #1 to Wordpress site #2, and have them be already authenticated for site #2 when they land there. IOW, I don't want them to have to authenticate twice just because I've relocated their app from #1 to #2. The Wordpress user tables will be replicated between the 2 sites, which may or may not be within the same domain.
Any ideas on how to accomplish this? (I can write Wordpress plugins)
I don't know enough about wordpress to answer definitively, but it is possible to use OpenID in an SSO (single sign-on) model wherein one of your wordpress sites (say WP1) acts as an openid provider for WP2. Once the user agrees to share their credentials with WP2 they should be logged in automatically. This is the method of authentication stack exchange uses; if you are logged in on stackexchange.com you will be automatically logged in on any of their other sites provided you have an account.
Janrain provides a library for php OpenId which I've heard good things about, personally (although I've never used it, but I have used OpenID with C#).