We had a similar thing happen to us when we were in Pickering. Andy's dad was still with us at the time, this was just before his knees gave up, so he was unsteady on his pins. We'd managed to find a parking space in the middle of town, and we wanted to go on the North York Moors railway. So we went to tourist information, and yes, we still had to pay, and yes, they had a wheelchair he could use, but they wanted it back in 2 hours!! What use was that. So Andy and his Dad both had a rant ('twas a sight to see/hear) and very nearly got in the car and came home. However, I suggested that we go to Grosmont (the other end of the line) and try our luck there.
After about 45 mins and lots of brake fade later, we got parked RIGHT next to the station. The guy taking money for parking wouldn't hear of it, as we had a bit of a rant at him, cos of how cr@p pickering was.
Moral of the story - if there's somewhere thats rubbish, touristy and ya can't get parked anywhere, try a few villages later, much better.