REDINGTON SHORES — The Town Commission recently decided to double the parking fee at County Park, from $1 to $2 an hour. Parking revenue is split between the town and the county. The commission also agreed to extend the parking fee to the other town parking lot next to the old Town Hall, which is now free, said Mayor Mary Beth Henderson. The rate increase is in line with other beach communities, Henderson said.Raising the parking rate to $2 an hour would give the town a substantial revenue boost, from $58,000 over the past year at $1 to about $116,000, Henderson said. And, she added, it would bring Redington Shores’ parking fee in line with other nearby beach communities.