Author's Note: It's been a while since I've written anything DBZ related. I'm trying to get back into the swing of things and came up with this story . A lot of alternate things occur in this story. This is just a simple explanation of what came before so that what happens in this story can be more easily understood. I have a ton of notes about it, but I tried to simplify things as much as I could. Perhaps later I'll post those notes as sort of an extra.
Disclaimer: I don't own DBZ or any of it's characters. If I did, I wouldn't be as broke as I am!
Love In The End Backstory Explanation
Frieza has not yet seized complete control of planet Vegeta and is more like a partner to them. Vegeta still works for Frieza on a more personal basis along with Nappa and Raditz. Much of the same events that occurred in the original Saiyan Saga still occur, however Vegeta falls in love with Bulma when she nurses him back to health after the epic battle with Goku ( a battle which is nearly the same as the canon) and stays on Earth. Vegeta's father, Frieza, and everyone else from his old life believe that he has been killed on his mission and don't pursue it further. Time passes, Vegeta lives on earth, fighting alongside Goku and his friends and has 3 children with Bulma: Trunks, Bra, and Vega.
During a different battle comparable to the one on namek in the canon story, Goku achieves super saiyan. The events occurring in the sagas following Frieza occur nearly the same as those in the canon(with the exception of Frieza being killed by Mirai Trunks, of course).
Our story takes place approximately 16 years after the end of DBZ. The GT events are totally nonexistant.
At some point Vegeta is located and receives word that his father has died and he leaves earth and his family behind to return to his planet as king. Trunks goes with him.
Vega, his youngest daughter, is 14 when he leaves.