Can you book a one-way ticket to the UK on a visa?

Your question suggests a significant misunderstanding of what your mother-in-law's visa allows.

Two years is the period for which the visa is valid. Individual visits on a Standard Visitor visa cannot be more than six months each. You are also not allowed to "live in the UK for long periods of time through frequent visits" (source for both claims: UK Government: Standard Visitor visa).

Even when somebody has a visa, they must still convince the immigration officer at the border that they will keep to the terms of that visa. One of these conditions is that they will leave the UK within six months. We cannot say for sure what will happen but if somebody arrives who:

• has family in the UK;
• has a one-way ticket;
• has no commitments in their home country that mean they have to go home on some particular day,

then the immigration officer could feel that they aren't convinced this person will leave the UK.

Presumably, if your mother-in-law had said in her visa application that her plan was to fly to the UK and stick around for maybe two years, she wouldn't have got the visa. The fact that she got the visa indicates that she must have described her plans and her situation in Turkey in a way that convinced the visa officer that she would abide by the terms of her visa. She should visit the UK in a way that is consistent with what she said in her application.

Finally, I'm surprised by your claim that it's cheaper to buy two single tickets than a return. That's very unusual: with a full-service airline, two singles are usually significantly more expensive than a return; with a low-cost carrier, they're usually the same price. The last time I needed to fly one-way, it was actually cheaper for me to buy a return ticket and not show up for the return flight.

UK doesn't put much stock in travel reservations easily cancelled for a refund. It's not nothing, but it's not much. If you think it's important, you may have another problem.

She needs to make her case to the Immigration Officer at Heathrow (or wherever she attempts to enter the UK). The IO will look at her story, facts and stuff, and wants to see that her apparent purpose corresponds with what's allowed on her visa, e.g.

• will do what was said at entry, and will return home as promised
• Won't live in the UK e.g. via repeated visits*
• Won't take a job in the UK, not even for family
• Won't rely on social services ("the dole")

For instance, they'll look at home-ties - does she have good reason to return home? And means - does her trip plan make sense given her financial situation? Her facts and story are much more important than her return trip ticket.

If a return trip ticket seems important, this may be because the rest of your facts are lacking. That would be a serious weakness in the application, and you should focus on that.

* if you were thinking that "2 year visa" means you can stay in the UK for 2 years, no. It just means multiple visits are allowed, and you don't need to apply for a new visa every visit. Each visit must still conform with visa requirements, law and common sense.