Permissions With Windows Groups And View To Other Databases

I am having a problem with permissions using Windows groups. I have a database (database1) that has permissions granted via Windows groups. Two groups (group1 and group2) are members of the db_datareader role in database1, and this work fine. Do to the number of tables that get created during our work, using db_datareader is the easiest way to keep up with permissions without creating a maintenance problem. Now I have a table that I want to add to this database, but I only want group2 to have select permission on this one table which is a problem because group1 has the db_datareader role. So I thought I could create a view in this database to the restricted table that I put in database2. Then in database2 I only added group2 as a user with the permission to select from this table. Unfortunately the group membership does not seem to get interpretted correctly in database2 and no one can successfult select from the view in database1.

In other words, user1 who belongs to group1 connects to database1 and cannot select from the restricted view -- this is what I would expect. However, when user2 who belongs to group2 connects to database1 they also cannot select from the restricted view -- not the behvior I would expect. Now, if I make user2 a user in database2 with select on the restricted table then user2 can connect to database1 and successfuly get data from the restricted view. So it looks like the fact that user2 belongs to group2 is never passed to database2 via the select from the view on database1. Is this indeed the way that Windows group security is working or is meant to work in SQL Server?

I realize I could solve this simplified version of the problem by creating my own role in database1 for group1 etc., but I am trying to solve a bigger problem in our environment that has hundreds of databases across numerous servers.

Thanks
Rob