I'm only partly in agreement with Woofgang.
There is no doubt that your daughter's contract was with the retailer and that it's their responsibility to provide a remedy. However the right to a refund (in respect of defective goods) only exists until the customer has legally 'accepted' the goods. The length of the 'pre-acceptance' period isn't defined in law but it basically provides a window for the customer to get the goods home and to check that they're working. So it's likely that a court would rule that your daughter had 'accepted' the vacuum cleaner within a week or so (i.e. once she had initially satisfied herself that it was working).
Once the 'pre-acceptance' period is over, the retailer remains responsible for remedying problems that occur due to an 'inherent fault' (i.e. something which was actually wrong at the time of purchase - such as the use of poor quality components or poor workmanship) for up to 6 years. However the customer has NO right to a refund; the retailer must only REPAIR or REPLACE the item.
Chris