You cannot appeal on behalf of anyone if the Notice to Keeper (NtK) is not addressed to you. In other words, only the Keeper can appeal. However, what is much, much more important is that you hopefully have not blabbed the identity of the driver.
The Keeper is under no legal obligation to identify the driver to an unregulated private parking firm. In the majority of cases, there is no Keeper liability if the operator has not complied fully with all the requirements of PoFA 2012. Only the unknown driver can be liable. So, what EXACTLY did you put in your correspondence with UKPC when you appealed 'on behalf of' your daughter?
If you follow the advice you won't be paying a penny to UKPC.