That Twitch in your Tail.

Prologue

*The Icejin's,  along with Frieza never had the chance to become rulers of the galaxy.

King Vegeta killed Frieza the minute he set foot in Planet Vegeta's atmosphere.

With the help of turning into the Legendary Super Saiyan.

Because of this the Saiyans became the superior race of the whole galaxy. They had the power to rule every planet they came into contact with.

More elites unlocked the Legendary Super Saiyan.

After some time King Vegeta, his son and his closest elites/ commanding officers figured out all the other Super Saiyan modes.

Making their race unstoppable.

King Vegeta decided if they would blow up the planets or they would set up some type of "taxes" for the residents of the planets to pay.

Earth and Namek being the lucky planets to have the tax rule.

Creatures from all over the Galaxy worked for the Saiyans, wether it be on actual Planet Vegeta or on the planets that the Saiyans owned.
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Gine and Bardock ended up not having Kakarot sent to Earth and had him in the rejuvenation tanks like what they did for Raditz.

Bardock also became the first commanding officer of the Kings Army him being below the King obviously. Brone became the second in command, and Paragus became the third in command. 

Kakarot, never ended up losing his bubbly personality and will to fight.
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When Kakarot turned into a toddler Gine found out she was with child for the third time. This time with a little girl.

Of course Gine was very excited. She was going to have a daughter!

She wondered what type of personality her new baby girl would have. Gine wondered if she would belike Raditz who was more like the traditional Saiyan, like his father or would she belike Kakarot, who may look like Bardock but had her own bubbly personality.

Oh she couldn't wait!*