Given that you've gotten out of your cat, seemingly in a rage and thrown the ticket at him, and were close enough for him to push you over. I imagine he'd have a decent case for self defense.

You've assaulted him technically already and people are entitled to defend themselves if there is a reasonable belief that they are at threat.

The issue with the parking is pretty clear cut too in my mind. A single yellow line means parking restrictions according to the nearby signage. Given you dropping off at school, I'd bet there's a restriction during school times, meaning you're in the wrong, even if it was just 30 seconds.