I'm working on a Multsite install with BuddyPress at http://www.yourcrimesite.com.
Through buddypress admin bar's login link
on both parent and child sites, the link goes to...
http://yourcrimesite.com/wp-login.php?redirect_to=http%3A%2F%2Fyourcrimesite.com
(don't know if that's important, but thought I'd throw it in there)
If a user logs in using that link, no matter where the user started (on their own site or the parent site), they are returned to the parent site, where their profile info and admin bar is then available.
>>I'd like the logged in user to be directed to the home page of the site they're associated with (not the parent site).
If I visit childsite.com/wp-admin, I'm taken to the child site's dashboard.
>>This is good
If I visit childsite.com/wp-login.php, I'm logged into the child site, taken back to that child site's homepage with the admin bar, profile, etc., shown.
>>This is good.
Logging out from a child site's Admin Bar returns me to the parent site.
>>Um...It's ok, but I think it would be better if the login/logout function hung around the child site rather than the parent site.
Logging out from the profile drop down with the site takes me back to the site's login page.
>>This is good.
Also, all of the users I have currently were manually added, and the sites manually added - not sure if that matters.