As I explained earlier, part of her problem with authority figures comes from a deep-set feeling that she was not being treated fairly growing up. It would seem that her grandfather was a dyspeptic jackass who thought that her turning out to be a girl was a dreadful inconvenience as well as a cruel injustice and a personal affront. Given that he had little time or use for anything in skirts and clearly doted on Alan and loved to tell her what she could not do, it doesn't take a genius to realize that someone as simple-minded as she is would lump anyone telling her that she couldn't do things with the hateful old pile of sludge. He, it would appear, is why the strip and Liographies are littered with hateful, inflexible, arrogant old tyrants who use 'tradition' as a club to smash down their children.
The other reason, of course, that being told that she couldn't do things was deemed so unfair that she's still angry at being told 'No' seems to be that, if I'm reading things right, she had planned her whole life out when she was five or six or so and reacted to any obstacle to said plan with something approaching blind rage. This tendency reveals itself in the nineties and beyond when April is treated like, at best, a hindrance because Elly did not expect to be a mother at her age. The clear message behind the observation that her birth on April Fool's Day meant that she somehow fooled all of them seems to be that she somehow made herself be born on purpose to make Elly's life bad.
We also have to contend with the fact that most of the people telling her what she can't do are of the wrong sort socially. Given that the only two police officers identified by name are Brad "Wrong Side of the Tracks" Luggsworth and Paul "Irish/First Nations" Wright and given that they are not good enough to be company really, it's sort of obvious that Lynn lets the same innate snobbery and racism that hates Mira for being proud of her obviously inferior background do her thinking for her.
That being said, of course, the real problem that the Pattersons have with authority is that they never really get to wield it. What we see in the strip is a clan of frustrated jerks bitching to anyone stupid enough to associate with them that they don't get to tyrannize other people in the cruel, self-absorbed way they want to.