Hang on, am I missing something? If you bought the trainers on 21 Dec, by my calculation that means that the exchange period runs out 28 days - 4 calendar weeks - afterwards - which is 18th January. The fact that there are Sundays and Bank Holidays is irrelevant, it's still 28 days, not 28 working days.
Why do you think that you can exchange them outside this period? - why couldn't you just have mailed the receipt to your daughter - or even scanned it and emailed it - so she could take them back herself.
IMO there is no solution, you are out of time. Your being out of the country won't be an excuse - the solution is usually to give the receipt at the same time but in a sealed envelope, in future, in case an exchange is needed.
JB Sports are within their rights - they don't have to exchange in the first place unless the item is defective, but they give customers a month to change their minds as a courtesy.