Unable to add db_datawriter to user defined role
JKay, you are a little mistaken about the syntax of this command:

EXEC sys.sp_addrolemember [ @rolename = ] 'role',  
    [ @membername = ] 'security_account' 


So in your particular case the command is:

EXEC sys.sp_addrolemember @rolename = 'db_datawriter', @membername = 'DR_User';