SQL Server User mapping vanished
I'm not sure if the issue is difficulty connecting a user to the login on database(db2) or if you are having difficulty unassociating the user with the schema dbo on database(db1).

It sound to me like the larger issue is connecting the user to db2.  If the user already exists on db2 you can associate them with the login using the command

EXEC sp_change_users_login ‘UPDATE_ONE’ , ‘sqlusername’, ‘sqlloginname’;


If the user doesnt exist in db2 you can create them using 

CREATE USER 'username' FOR LOGIN 'loginname' 
WITH DEFAULT_SCHEMA = 'default schema name';