Using the reference card a few times at least isn't a bad exercise to go through in the overall journey towards photographic enlightenment
The whole topic of WB "correction' is a pet peeve of mine. For example you mention the dog having black fur "with a lot of blue in it". In-fact we know that dog's fur isn't blue. It's black. The blue that we see is bluish light that is reflected off of the shiny oils on the animal's fur. Some people would argue that you should correct white balance to remove the blue cast from the fur. And in lieu of any other neutral point in a scene that can actually be a good way to find true WB(try it). But in fact the blue/black is what our eyes perceive. So why would we want to "correct" it? However, the blue/black fur can be a clue for you. The fur is reflecting blue light. So, in truth though you may be thinking that your green cast is due to reflecting green light, it may in fact be due to the scene being lit with cooler light than you think and the camera WB is correcting for it (i.e.shifting toward yellow).
Another exercise you may want to go through for informational purposes it so compare how the RAW files are rendered by Nikon's (free)software versus your RAW converter of choice. You may find that your RAW converter is rendering the images with a color/temperature bias. Not suggesting you switch software. Just to gain understanding that there is no true "standard" conversion.