As RPCrow stated the main problem is the green tint from the color cast of the foliage.
I would first work on remedying this in camera as even with PP your tones will still be off a little bit if trying to keep the background colors accurate.
As stated above, proper exposure in camera will help negate an odd tint from the shadows.
#1. Be at the edge of the shadow (under tree etc) rather than deep into the shadowed area.
1a. Lay down a white sheet on the ground. This will reflect the color of the sun, rather than green grass and trees.( this may cause a little bit of ghost/under lighting catch light)
1b. Even better, use a reflector (can be under $20) or even flash set to negative -1/3 to -2/3 flash exposure compensation. This is just a starting place without having to invest very much money.
#2. A hardware monitor calibrator is the way to go. The more $ you spend on one the more accurate it will be for printing the image.
You can get one for under $100 that will at least get the colors accurate, the more expensive ones will get the exposure correct as well.
If you do this, you will find that you will not need the WB card as often, though it is a life saver and a cheap investment. Where i find the WB card the most helpful is in getting the tint correct, then i adjust the temperature of the image to taste. (shooting in raw and using a good PP software will make this make more sense)
#3. As stated above Lightroom is the best bang for the buck for photo editing. LR 5 is under $80, LR 6 is under $150 and LR cc2015 is by monthly subscription. Try to buy LR 5 or newer as the newer features can make life easier. ($ USD)
#4. Make a couple of cheap prints. I don't know if you have your own printer, but your local Costco, Walmart etc will print a 4X6 for $.17. This way you can see how far off your monitor and your eye are. Be sure to turn off the auto color correct when you order the prints.
