The scene isn't a straight white balance issue, which I think is where the software is failing. As you can see in your corrected image, you're getting what we used to call in film a 'crossover' effect- where the highlights and shadows are opposite hues (in this case green and magenta, respectively). What happens then is that if you correct for one, the other looks worse. If it was a still, you could correct by manipulating the two separately, but I don't know if it's possible with your software.
One thing you could try (if the software allows) would be to decrease green saturation while playing with the color balance.--