iTunes for Mac is not connecting to iPhone 4s since screen & battery were replaced.

Before my husband took my 4s to a 3rd party repair shop, I backed it up to my iMac via iTunes then "erased all content and settings."

Initially, it was just the screen that was to be replaced but hubby decided to get the battery replaced too, as it has been performing poorly for a few months.

Anyway, when it was returned I plugged it in to my iMac, launched iTunes to restore from the recent back up and got the following message:

The iPhone "iPhone” cannot be used because it requires a newer version of iTunes. Go to www.itunes.com to download the latest version of iTunes."

I updated the iOS software to iOS 9.1 and then "erased all data and content" again, as per Apple Support instructions. Then went through the iPhone set up screens and when given the option, I clicked "restore from computer". It asked me to connect to iTunes but I then got this mesage:

The iPhone “D C's iPhone” cannot be used because it requires a newer version of iTunes. Go to www.itunes.com to download the latest version of iTunes.

My 4s had been named "Dee's World", as had my previous 3GS, so I'm not sure where this new name came from (?)

Luckily my contacts and calendar data are regularly backed up to iCloud, so I haven't lost that data. I've managed to download all my purchased apps over wi-fi but important data on a couple of health apps has been lost.

I have tried various options (as found on Apple Support) all evening to try to get iTunes to connect to my 4s to no avail. I've restarted my iMac and restarted iTunes. I've even gone to "Find iPhone" and it shows two devices - "D C's iPhone" and "Dee's World". However, the image that appears for "Dee's World" is a 3GS and it says that it is offline.

I'm completely confused as to what's happened.

Any ideas as to how I can get iTunes to connect to my iPhone so that I can restore from my recent back up?

Thanks in advance.

Dee