It's not your house; it's your parent's. Notwithstanding, your parents don't own the sidewalks; the city does. You parked on their property, so they ticketed you in accordance to the laws you agreed to when you became a licensed driver.
I don't see what's so difficult here.
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I'm not questioning the validity of the ability to be ticketed for parking how I did.
It's just a real bullshit thing for a cop to do.