You should always try Plan A first. Find out who the landowner or their managing agent of the retail park is. If there's an advertising plinth near the entrance, usually at the bottom of that will be the managing agents contact details. You need to contact them and explain that the driver was not aware of any restrictions due to poor signage. Evidence that money was spent and that being a patron of businesses at the location shouldn't come with an added £100 invoice from an unregulated private parking company.
You should also complain to the businesses where money was spent and tell them that you, your family and friends will not be coming back for future business if this PCN isn't cancelled. If they wonder why their footfall decreases, they can thank the unregulated private parking company and whoever contracted them.
You can appeal to UKPC and have that rejected, which will get you a POPLA code for a secondary appeal, where you have a slightly better chance of success. POPLA is not independent and is looking out for its paymasters interests, so don't be surprised if that appeal fails too.
No one who is receiving advice on here pays a penny to UKPC. If the POPLA appeal fails, this will eventually end up being a debt claim in the ultimate dispute resolution service, the small claims track of the county court. The claim will be issued by DCB Legal and, as long as it is defended with any old defence, it will eventually be discontinued. I say this willower 99% certainty.
The Notice to Keeper (NtK) is PoFA compliant so not "get out of jail" card there. As you mention, signage is always the way to go with any UKPC PCN. Their signs are terrible. However, you have to convince the POPLA assessor why.
For now, simply appeal to UKPC as the Keeper with the following whilst you carry on with Plan A:
I dispute your 'parking charge', as the keeper of the vehicle. I deny any liability or contractual agreement and I will be making a complaint about your predatory conduct to your client landowner.
Any signs at the location do not comply with the requirements of PoFA 2012 2(3)(b)(ii) as they do not adequately bring to the notice of the driver the charge for breach if any terms,
Since your PCN is a vague template, I require an explanation of the allegations and your evidence. You must include a close up actual photograph of the sign you contend was at the location on the material date as well as your images of the vehicle.
I suggest you cancel the PCN or issue me with a POPLA code.