"unfair parking fine"

Whilst I appreciate the fine has not come from the hospital itself, it is as a result of spending the night in hospital the fine has come about. My daughter was in hospital on 25th August for an operation and we had to stop in overnight. On 26th August her grandfather came to pick us up and parked in the drop off/pick up bays. When we had got to the car within the 20 minute slot my daughter, aged 5, announced she needed to go to the toilet. Although she had already been to the toilet prior to leaving the ward, she needed to go again. We went back in to the hospital but unfortunately she was a little constipated due to her being nil by mouth the previous day. You really cannot rush a 5 year old when they need to go. As a result of this we have now received a parking fine for staying 11 minutes over the 20 minute stay. I honestly don't think this is fair and I can't afford to pay this. However to appeal the charge it will take me over the 14 days for the lower amount and it will increase to £70 if not paid within 14 days. I feel like I am being blackmailed into paying. Of course you can only appeal in writing - there is no human to talk to to try and discuss the situation.