How to troubleshoot db/app latency during transaction log backup
It sounds like your transaction log probably has a lot of VLFs on it which causes the SQL Server to take a hit when doing the transaction log backups.  You can find this out by running

use {MyDatabase}
GO
DBCC LOGINFO
GO


The important part to look at is the number of rows which are returned.  If there are more than about 100 rows returned then you've got problems (please comment with the number of rows that are returned).

The fix is pretty easy.  Make a note of the size of the transaction log.  Shrink the transaction log down to as small as possible (the above command will return 2 rows).  This is done using the DBCC SHRINKFILE command.  You may need to run the shrink command a few times to get it small enough.  Try waiting a minute between shrink commands for the logs to cycle and run a log backup just before running the shrinkfile command.

DBCC SHRINKFILE (2,1)
GO


Then once the transaction log file is as small as possible grow the file in 8000 meg chunks using either the GUI in SQL Server Management Studio or by using the ALTER DATABASE command.

ALTER DATABASE MyDatabase
MODIFY FILE (name='MyLogFile', FILESIZE=8000MB)
GO


If you need the file to be larger than 8000 Megs do 8000 megs in size, then 16000 megs in size, then 24000 megs in size always growing 8000 megs at a time.  Compared to the prior size of the transaction log grow the low to the 8000 meg mark past the size that the log was.

If this doesn't do the trick let me know.