wife is a hair dresser and says that if the green is from copper pipe corrosion, then you can try to get her molasses purifier shampoo, which will take the majority of it out. If they try to color over her hair and there is a lot of copper, the color can react with the copper and actually burn the hair.
to take out the green, get her molasses purifier shampoo and that should take the majority out, but the wife says copper coloring is really hard to get out.
She also asked if you wife swims much? It could be Chlorine, but if she is not swimming a lot, then it's probably not the problem.
The water softener is acting as a filter, you can either redo the water softener so it filters out the copper, or just actually filter the water with a normal filter.
if the green is due to a corroded pipe, then you need to filter at the faucet, not on the incoming feed.