The firing is irrelevant. In the absence of a warrant, a police officer must have probable cause to believe that a crime is either being committed or is about to be committed. The officer in question admitted at the scene that he had no probable cause. He therefore had no right to even ask her to identify herself. Arresting her is exceeding lawful authority and I'll bet her action will be successful. Any prior altercation with the law is also irrelevant.
For all their nastiness by virtue of the fact that they're incredibly overworked and underpaid, I have to hand it to the US Park Police. The last time they came up to question me on the C&O National Historical Park towpath, they at least knew the law. If you're a commercial photographer you have to have permit to photograph there. They asked me, "What do you do with the pictures you make?" I said I frame them and put them on the wall. "Do you sell them?" "Don't I wish!" I replied. They didn't like it, but they let me keep working. A universe apart from the rent-a-goons at the National Arboretum to whom tripod=commercial=pack it up, buddy.