HOAs somehow can prevent you from parking stuff on your driveways, even though you are the prez....but they cannot give you any kind of shit for parking on public property (streets) your trailer or car or anything else if properly registered.
If it really was the case that your car was there for too long, then yes the cops can tow it away on public property.
a buddy of mine in Westerville had his stupid neighbor call cops on him and HOA for parking is trailer on the street....when the cops showed up (because they were bored) they laughed with him when they told him that legally, no HOA or they could do anything about the trailer on the street as long as it is moved every so often. They told him that lady had no standing at all for complaining. Since then, the lady has not called the cops on him for the trailer