So, a marked out bay with signs for "No Waiting except taxis", and "Taxis" painted on the edge of the bay. The carriageway text and markings are a bit worn, but IMHO would satisfy an adjudicator. The PCN looks OK with no fatal errors of content.
Well, sorry to say it, but you don't seem to have a very robust case to take to the Traffic Penalty Tribunal, and if you do, the £70 is payable if you lose.
However, you haven't told us why your wife parked there. If she parked, took your daughter into the centre, then came back leaving her with staff at the centre, then you can claim 'assisted alighting". Otherwise, I see no case for cancellation of the PCN.