we have an Iphone 4s runninig old 4.2
Sounds like an iPhone 4, not 4S.
iPhone 4S was released with iOS 5 and will not run an earlier version of iOS.
We know we have to run this through Itunes, so do setup to use a different Apple ID to synce with a computer that already has its own Apple ID signed in?
Not sure what you mean. You don't need a different AppleID.
Plug in the iPhone, open iTunes, select the iPhone and click Update.