For Broly if he got his own movie I'd basically scrape his origin from the animated movie. He'd have been at least eight when Planet Vegeta was destroyed & instead of just hating Goku, he hates Vegeta as well because he's a cocky little brat that gets what he wants. As for his hatred towards Goku, I'd only have him hate him because one did Broly witnesses his father challenging Bardock in which he loses & this angers Broly who goes to kill Kakarot but is called before he can commit the act or something to that extent. Basically, Paragus speaks out of term during a meeting of the Saiyans which causes King Vegeta to want him to be exterminated. The most powerful soldiers who protect the king commit the act, believing both Paragus & Broly to be dead. That same day Planet Vegeta is destroyed but Broly, still being alive, harnesses enough power to form a shield around the two. If I were in charge, as Broly grows up he'd slowly go insane as his power grows & he'd have more hate towards Vegeta than anyone else.