No 'sofware update' section on my iPhone 4s - how do I update OS?

If your iPhone looks like this:

Or this:

Then it's an iPhone 4 and should be upgradable to iOS 7.1.2

But if it looks like this:

Or this (white plastic back):

Then it's an iPhone 3G and cannot be updated past iOS 4.2.1. Which would explain the message you're getting from iTunes!

See this article for instructions: Update your iPhone, iPad, or iPod touch

As KiltedTim said if you currently have an earlier version of iOS than 5.0 then OTA updates are not available so you have to use iTunes as described in the above tech note.

Incidentally, for major version upgrades (e.g. 4.x to 7.x, or any update that involves incrementing the major version number, like the upcoming 8.0 release for example) I strongly recommend you always perform them via iTunes, even when OTA updates are available. Major version upgrades are usually more reliable when performed via iTunes, and they don't require as much free space on your iPhone either. More minor updates (e.g. 7.0.x to 7.0.y or 7.0.y to 7.1.x) are usually safe to perform OTA directly to the phone.

I checked the 4s info and that model originally came with iOS 5.0, so you must have at least that version installed. And that's the version that introduced Over The Air updates so you should have that available too.

Check what version you currently have installed: Settings/General/About/Version. You should find the OTA update option under Settings/General/Software Update. As I noted previously if you are on anything less than 7.0 currently then use iTunes to update to the latest version - 7.1.2 (until next Wednesday when it will become 8.0).

tonefox is right, you appear have an iPhone 4, not a 4s. iOS 4.2.1 was never released on the iPhone 4s, that model originally came with 5.0.

Without knowing what exactly your mother's iTunes problems are all I can suggest is to make sure she is on the latest version of iTunes - currently that's 11.4 - and OS X 10.9.4. (It sounds like your mother isn't big on updating her software. You really need to talk to her about that... 😉)

part from that, i've tried updating on iTunes using my mum's macbook (had to download iTunes ontofirst) but i just get told i have the most recent version of 4.2.1. baffled now.

The iPhone 3G only went up to iOS4.2.1

What is the model number under

settings>>>general>>>about

Over the air software updates did not become available until iOS 5. Plug it into your computer and update it with iTunes.

Starting to look like an iPhone 4....

try through iTunes. when u plug in, if ur device needs to update it will tell to download and update