To be honest I am a big furry pet fan have had 5 hamsters in my time and I would def say it was not your fault the shear fact that the previous hamster lived 3 years proves the fact that you and your sister know how too look after a hamster and the basic requirements of it lifestyle and the do and don'ts.
Also as soon as a heard 'Pets at home' I became worried, it be honest they dont have many fans this company, they are know for not looking after their animals, and providing poor care to the animal residents. A pet from them is an unhealthy / ill pet in mainy peoples views.
I am in no doubt that the death of the hamster is down to 'pets at home' and not down to you. Yes you should get a refund but I would ring first because I would worry they might suggest 'proof' and a 'hamster body' brought in to the shop, the fact they might not take your word for it, is bad enough as it is, but companies are companies.
I cannot see taking the poor dead thing in would be good for your sister to witness if it hasnt been buried already anyway.
Even if their refund process is good and they do give your money back I recommend not to buy another hamster or animal from them please. The fact one has died in 24 hours is proof, how many more die and they hide them out the back (I have heard of rumours concerning this).
Try another pet shop, or even ask other people where they got their hamster, recommendations always the best. Good luck and tell your sister it was an old hamster bought by mistake!!! Talking about that it reminds me 'Pets at home' do take in unwanted pets from what i have seen in my '1' visit to a store in western-superware, They do not label them as unwanted or returned but you can see they are old and a price is just slapped on them. So i suppose there is a chance it is an old one and they wanted to get rid of it.
Good luck