I think you have answered your own question there....... what you bolded is, in my opinion, the relevant text of the law. The April 8 grandfathering of the local prohibitions (if any) is what will trip you up so you need to research city ordinance to find out if there is actually anything in place for that location. Yep, a huge pain in the axx. Gotta love it don't ya! Here in Knoxville there are such parks with bans in place and you best know which ones they are....... and I am still not quite sure about which ones they are. I just don't get why our benevolent rulers wont go along with full state preemption to make the carry laws the same across the state. Good luck in your further research.