The way I take it, "You made a rebel of a careless man's careful daughter" means the narrator has gone against her old beliefs. "careless man's careful daughter" probably means her father left her mother and her (probably for another woman), and growing up with this experience, she has become a careful girl, as in vowing to herself that she won't fall for a man and become a victim like her mother ("Braced myself for the 'Goodbye' / 'Cause that's all I've ever known"). But this new person she met has changed her cynical attitudes about love, because unlike her father he really cared for her and never left her even in difficult times. So she no longer thinks the way she used to - i.e. she has become a rebel. This is an oft-repeated theme. The Goodbye Girl is an old movie about this very exact theme. And Thelma & Louise is one of the very opposite kind, about two women who become literal rebels revolting against the unfair world (in their eyes) and choosing to drive off a cliff in the end rather than submitting to it.

To me it means that, overcome with infatuation for the guy, the girl abandons caution and convention and decides to take a chance on his love. Based on her past, such behavior is not what people would have expected her to do, but she throws caution to the wind, just as her father did before her.

I interpret it this way. First: "a careless man's careful daughter". The implication is that children go opposite their parents. A careless man has a careful daughter. To say, "You made a rebel of" that careful daughter means that the boy nevertheless turned her into a rebel, despite her previously being "careful".