How can I "Delete the backup" without deleting all the information in it?

For the past 2 weeks I've been tring to update my iPhone 4S and my husband's - both are still on the 6.0.1 OS - to the updated OS. It seems that this version of OS has done nothing but create problems with updating our phones. However, previously today, I was unable to back up my phone but it would not update the OS. So, I logged out, etc, and restarted my computer. I'm still getting the message "iTunes could not back up the iPhone...because the backup was corrupt or not compatible with the iPhone. Delete the backup for thie iPhone then try again." Which is the same message I've gotten ever since I updated to the 6.0.1 OS. I'm at the point now where I'm ready to give up and delete the back up but how do I delete the backup without deleting all the information in it? When I last backed up my iphone I removed some of the apps I had on it as well as some pics to make room for audio/video I want to add. So what happens to the apps & pics I took off my phone? Will I lose them all?

I've spent 6 hours off and on today trying to fix this issue - repeatedly trying to get it to work, shutting off my computer, etc. - and that doesn't take into account the hours I've spent the past two weeks trying to get it to work. Now it's past my bedtime (I have to get up at 2:30 a.m.!) but I'm still here trying to fix my phone! It makes me want to turn it back in. I've not heard that anyone else with these problems. The Galaxy SIII doesn't seem to have them. I wonder if I bought the wrong phone? I SO need to get to bed and not be wasting time doing this.