Did you actually watched the whole S2? I don't get where you're getting much of what you writed.
Yes ... she tryed to like her dad, he fucked up. She them tryed to like her mom, she fucked up. Then her dad kinda saved her and became good and .... she mindwipped him.
I don't know about you, but I don't want to mind wipping someone I LIKE. And that was someone who saved you from your mom that wanted to kill you.
So ... the name "Daisy" represents everyone that she is not a fan of.