I would also fall on the side of 'pay it now'. Without getting into any moral arguments about whether it's right to pay the £80, it's the only route with a guaranteed positive outcome - although the OP will be down by £80, they and their daughter will have certainty that the matter has been resolved. Given that there is no dispute that the OP's daughter travelled in breach of the rules by not having her ticket available for inspection at the appropriate time, any other option relies on the railway not enforcing their legal rights - and while it is unlikely (even highly unlikely to the point of almost impossible) that the railway would seek to pursue a minor through the courts it is not absolutely impossible. Without conceding and paying the £80, then until the dates for prosecution or civil action have passed the OP will not be certain that this time the railway will do what they normally do.