SQL Server 2008 R2 - VLDB Backup Strategies
Log shipping to the primary site then doing backups isn't going to work as you can't backup a database which is waiting for t-log backups.

With SQL 2008 your only option would be to backup to local disk, have the storage array (I'm assuming that you have a storage array in both sites that can replicate data between the sites) replicate the backup LUN to the array at DC1.  Then during the day once the backup has been fully copied over to DC1 snapshot the copy of the LUN at DC1, mount it to a server at DC1 and backup the database to tape.

Another option would be to upgrade to SQL Server 2012 and take advantage of AlwaysOn Availability Groups which would let you replicate the data to a server in DC1 then you can take your backups from the server in DC1.

A third option would be to buy more storage at DC2 and keep more than two backups around.

A fourth option would be to move the application to DC1 and run it from there.

A fifth option would be to buy a tape backup unit for DC2.