Copying a restoring database in SQL Server 2012
If you want to (1) maintain your log shipping environment and (2) want to have a read/write copy occassionally you will need to maintain 2 databases, TargetDB and Target2DB.

Question, could you just restore the backup from the Server A SourceDB to Server B Target2DB?  That might take a little longer, but there are fewer moving parts running all the time.

If read/only access would be sufficient, you can create a database snapshot for reading purposes. This creates a point in time snapshot of the database, supported by the .SNP file that maintains the needed data to support the snapshot, despite other changes coming in.

CREATE DATABASE TargetDB_Read
  ON (NAME = 'datafile', FILENAME = 'F:\TargetDB_Read.SNP')
  AS SNAPSHOT OF TargetDB


Note: You can create several snapshots if needed at different points in time. In that case, name the snapshot for the time it is created.  E.g. TargetDB_0800.)  See:
http://technet.microsoft.com/en-us/library/ms175876.aspx

Of course if you bring Target2DB online so as to do Read/Write, once you are done you will need to restore a Full backup of the SourceDB as the new Target2DB, then catch up with changes through restoring Differential and Log backups until you are once again ready for log shipping.