It would be great to see Paragus and Broly observe the Z fighters at the tournament, and they could leave the tournament, because Trunks was kidnapped. Then it could turn out that Paragus took him to their kingdom, and was treating him like royalty, being Vegeta's son. He could tell Vegeta about his history with King Vegeta, and lie about not wanting revenge. Paragus just wants to bring the Saiyans back to their rightful place as the strongest warriors of the universe, and wants Vegeta to rule them, being the rightful heir to the throne. I would rather them not have SSJ2 at all for anyone, but Gohan, and then convince Vegeta to return to his roots. Then you can get the Goku vs Vegeta rematch, without having to worry about any powerups, plus you can keep other characters relevant, since their wasn't a big power increase. Piccolo would actually be stronger than Goku, being that Super Nameks are much stronger than Super Saiyans. You could have Ten, Yamcha, and Kuririn going up against Paragus' troops, or helping them out in the background.
I want to see something similar to the Hunger Dogs on Apokolips, where the civilians are all slaves and treated horribly, yet they all have Stockholm Syndrome, still worshipping Paragus, no matter how evil he is.
While off planet, you could have mind controlled Broly, being held off by Piccolo, Gohan, and Android 18. I would love to have that mentoring role of Piccolo for Gohan, and have him setting up strategies, mid fight. There could be a bunch of criminals taking advantage of the destruction caused by the mind controlled Broly, and then have Master Roshi lead the World Tournament fighters to help fight them off. Chi Chi could help the injured, while Bulma starts mass producing Saiyan armor and weapons to give to civilians, so they can defend themselves against soldiers from Paragus' kingdom, as they try to take over Earth. Then you can have a moment when Paragus stabs Trunks, like King Vegeta did to his son, and Vegeta tells Goku, Ten, Yamcha, and Kuririn to leave the planet, because he's going to blow himself up along with the planet. Then Broly's mind control could be broken, and then back on earth they have to deal with LSSJ Broly. Broly fights out of self defense, because he doesn't understand why he's being attacked by Gohan, and Piccolo. He could kill Piccolo, and after seeing Gohan's reaction to Piccolo's death, and realize their not evil.
Those are just some ideas, I'm throwing out there, but I think it would be a really neat movie!