I have a SP2010 On-premises setup here and recently used stadm to enable the people-picker to resolve users from a trusted domain. This is now resolving fine, however, I've added a test user from this domain to the Contribute SP group but cannot login to the site, it just repeatedly prompts for credentials. I've used the "Check Permissions" tool and SP is reporting that this user has Contribute and Limited Access through relevant groups so as far as it's concerned I should be able to log in but I can't.
Removing this user from this group is reflected in the results of this tool as expected.
I've left this overnight to make sure it's not just down to a timing issue but doesn't look to be the case.