You need to be more careful when posting images of documents that contain personalised info such as the PCN number and your car reg. Someone with less scrupulous intentions could easily get in and mess your chance of appeal.
You need to go to
https://ukpcappeals.co.uk in order to appeal.
However, have you tried plan A yet? Go to the store or find out who is the landowner or manager and ask them to get the PCN cancelled. It really is a de minimis issue and just goes to prove how much these scammers will try to extort money.
If you've had no luck with Plan A by day 27 of the issue date of the Notice to Keeper (NtK) then you should do the Plan B appeal to UKPC. Just in case you are not aware, you are dealing with cowboys and scammers (Hansard) who really do not care about any mitigating circumstances. If/when they reject your Plan B appeal, you then move on to your Plan C POPLA appeal.
If/when they reject that you go through the "limbo" stage where you just have to weather all the useless debt collector letters which you can safely ignore. If/when either UKPC themselves or through their solicitors, DCB Legal, you are issued with a Letter of Claim you come back for advice. This is the Plan D kicks in and is a guarantee that they will eventually discontinue.
A robustly defended claim from UKPC directly or through their DCB Legal pals, will result in a discontinuation before any hearing. They are hoping that you are low-hanging fruit on the gullible tree and will capitulate at the first sign of any threats and pay up. Hold your nerve and they will will be the ones that capitulate in the end.
As it is your wife who is the registered keeper, all correspondence has to be in her name although you can do it all for her. The NtK is basically PoFA compliant (except for a technical failure which they are likely to ignore) so the keeper can be liable for the charge if the driver is not identified. In all cases it is the driver who is liable and transferring liability to the driver if your wife was not the person who parked does not really matter.
Any appeal for Plan B and Plan C must show that it was impossible to park within the bay and have space for a passenger to enter/exit the vehicle due to the poor management of the parking spaces by the operator as is evidenced by their own photos. In fact, the vehicle is not parked outside of the bay as the cars wheels are on the line itself. Therefore no breach of terms has taken place and there was no reasonable cause for the operator to request the keepers details from the DVLA in breach of the KADOE rules and the keepers GDPR.
Additionally, the UKPC signs breach their own ATA, the BPA, Code of Practice in that they are illegible unless you are within 6 inches and your head is at least 7 feet above ground level.
For now, concentrate on Plan A.
Follow the advice you get here and you will not be paying a penny to into the UKPC scam.