Disclaimer: I don't own DBZ.
Abused Frieza who isn't bad and later gets accepted into the Z Warriors.
Now THIS. THIS is something that will be difficult. I'm talking about completely changing Frieza. Let's start from the "Destroying Planet Vegeta.". Cooler did that. He was starting to fear the legend of the Super Saiyan. He also took his little brother along because he was too gentle and soft hearted like their mother. Cooler wanted to make Frieza he him and their father King Cold. The plan didn't work. He even found out that Frieza let a few saiyans escape. Furious he and his father beat him up for that.
Years later Cooler finds out about the dragon balls (Same as cannon.). He takes poor Frieza along too (Also, like Cooler Frieza by now is constantly in his fourth form because he has so much power he can't detransform) to try and show him how to be like him and Cold.
Of course shit happens but instead of Goku defeating Frieza he defeats Cooler with Frieza's help.
(Also, how Frieza looks is basically the same Frieza from DBZ but more white, the shiny purple places are green and the eyes are seafoam green. Also black lips.)