It is clear that an 'ERROR' has been made. It's been made by you, or the holiday company, or by you both. Error is a ground that can have a contract set aside - i.e. as if it never happened. or, it can be relied upon to enforce the contract. Confused?
The route to solving this problem exists in idfentifying the party (or parties) who has made the 'ERROR', and whether it was induced or uninduced.
It seems that the holiday company have made the error - they thought your sister would be sixteen at the time of departure. But what led them to believe this?
If this error was induced by you, they win, and you pay - or at best you lose your deposit and they sell the holiday to someone else.
If their error was uninduced by you, you win, they pay, or, (if you wish) you get a refund. But proof may be a problem. Can you really prove that they knew your sister would be 17 at the time of departure even though they quoted a price for a sixteen year old as she was at the time the contract was concluded? My guess is that the contract will deal with such situations.
If the error was mutual, the contract never existed and whichever party is out of pocket should be refunded.
However, the terms and conditions of the paperwork will probably prevail. My money would be on the holiday company who have probably designed their contracts to contain standard conditions and exclusion clauses to deal with such questions as have been posed. They're smart like that!