In my case it's Heather and her father Corey overall: Corey was just a normal person like you and me and bought the Ruby Ring to propose to his wife, Elena. But when Heather was born, Elena's life was cruelly taken away just because of the ring. This was a final blow to Corey, who would raise Heather in his ways and become the cynical person, whe met and joined Team Meteor to take it back. The two different routes involving the police officers is depending how tragic it is: 1. In the Police Found Route, he gets exposed in front if his OWN daughter (which mentally broke her down and runs away) and he despises us for taking his only happiness away and wanted to kill us (since we found all the missing officers). 2. In the Police Farce Round, you never find out that he's an agent and not exposed in front of his daughter. Will this lessen a bit the damage for Heather and cannot clearly see that (especially in your first time). But think about the cause behind: Her mother died because Team Meteor wanted the Ruby Ring, Corey gave her as a proposal gift and growing up without a mother is the most terrible thing, that can happen to a child. This of course took a huge impact at Corey, who changed drastically and became very vengeful towards his wife's murderer and joined them for that. Despite having genuine and good intentions, he clearly had to seek help for the issues than commiting suicide. And Heather? She was raised by a nihilistic father without a mother, who has the mindset "The world is cruel and reality is harsh", forbidden her to do things and sent her rules without explaining her the reasons for. As a result, she became very rebellious and refused to listen to others. I think the whole 'hero child' act is simply a way to cope herself with problems and her pain, to give herself some meaning perhaps. But the real misadventures started after Corey's death: We, Cain and Shelly tried to resure her safety, but she ran off and caught taken by Dr. Sigmund and given an electroshock therapy, making her mute. After the events of Yureyu, she ran off again because she felt ashamed for the trouble she caused. Hadn't she ran off from her problems and being honest, than none of this would've happened.
Even if she came to releasing this during the Ametrine Arc, when being locked by Blake, Heather symbolises helplessness and loneliness because having no good parental guidance will cause further problems later on and you'll have some real trouble because you're actually helpless against this all alone.
As for Corey, his wife's death did tore him apart, that his mind was filled with revenge for that. And this influenced his guidance for Heather a lot. And it didn't end very well for him, regardless in both routes. Had Elena (Heather's mother/Corey's wife) survived, than most of the Molinar drama wouldn't existed.