READ THIS FIRST - Private Parking Charges Forum guideWhat did the hospital PALS say when you approached them about this issue? If you haven't asked them to get the PCN cancelled, then you should be pro-actively getting on their backs about it.
It sounds as though you have now received an N1SDT Claim Form from the CNBC if the cost has gone up to £257. Probably too late for PALS to do anything about it, even if they wanted to.
Please show us the original Parking Charge Notice you received and the Claim Form, if you have received one already.
They can't "legally force" you to pay the "fine" because it is not a "fine" at all. What was originally received was either a Notice to Driver (NtD) that was affixed to the vehicle or a postal Notice to Keeper (NtK). Either way, they are not "fines" at all. They are speculative invoices from an unregulated private parking company for an alleged breach of contract by the driver.
If they have issued a debt claim, it is a civil matter and is defended before a judge decides whether you owe the debt or not. The county court small claims track is the ultimate dispute resolution service and you should not fear it, especially if you feel you are in the right.
However, we have nowhere near enough detail in order to begin advising you on what you myst do next. Please answer the questions I have already asked above and also tell us the name of the parking operator and who, if anyone is representing them.