Your narrative tells me you are a medical professional, or doctor. I'm also presuming you work at the Doncaster Royal Infirmary and that they charge employees as well as patients and visitors for parking. So you park in several places in city streets around the hospital over the working day.
If the above is incorrect, please tell us the situation.
It is quite clear to me that the circumstances in your narrative present as very strong, indeed compelling, circumstances that should, in a kind world, justifiy cancellation of the PCN. However they are arguments in mitigation. You parked knowing it is a 3 hour limit, but work circumstances were such as to prevent you returning to your car to park somewhere else near the hospital.
What the above means is that you can submit representations to the council, but acceptance of mitigation is their power alone, an adjudicator at the Traffic Penalty Tribunal cannot rule based on mitigation grounds.
On the other hand, any errors or omissions in Doncaster Council's management of the enforcement process would be a procedural impropriety. This is one of the statutory grounds of appeal an adjudicator can decide on. This is why we always like to see all sides of the PCN to check it for fatal errors of content. So please post the reverse side of the PCN.