In my study of bugs, and my father cared for a 226 acer farm which I grew up on, we had to deal with these bee's on a daily base's. I hope this will help you out. By understand their behavior is always the best line of deferences.

If there is a way you could wait till colder weather when the bee's become non active, you have a better chance of getting rid of them for good. In order for them not to rebuild the nest, the nest needs to be removed all the way, till thats done they will keep building it back. Still even with that they may need to spare the area to discourage them from doing so. Once that nest is down they will seek out another area to build in. Got to keep those eyes open for new ones. If you see any, the sooner it's removed the better, within time they do get the hint. Hornets are nothing to play with. They sting till the stinger falls out or it's ripped out. Unlike many common bee's. Even then people need to be careful around them, these bee's have been know to cause a reaction in people that are non allergic, and once to many stings encored it can be fatal.
There are stories where these hornets are known to file out of their nest by squadrons in hot pursuit of those who dare approach too closely. Bald-faced hornet nests had best be left alone. This nest houses a queen along with 200 to 500 members of the brood depending on the nest size at times even more. Simple sounds of a mower, or a walk by can send them into a full attack mood.
These bee's function of aggressions are set off by vibrations. In one study I have seen, they attack a speaker that was place under a nest covered in latex wrapping to count the stings that would be inflicted. It WASN'T A PRETTY PICTURE. They stung it over 300 times before backing off of the speaker. This test was done with a nest only a little over a foot long. Further testing was done on the venom, showed to be highly toxic and equal to the bit of a King Cora snake bite. If enough stings are inflicted it is lethal even to large humans.The study also proved that these bees are able to live following inflicting multipliable stings, as long as the stinger remained in-tacked they can regenerate the venom. Your best line of defense's is to remain away from the the nest till cold weather, and temperatures are below frost levels. They become sluggish in movement doing this time. But at 32 degrease they lay into hibernation state for the winter months till temperature rise above 32 degrease. Doing the later month before the temperatures drop, they become even more active collect food for the colonies.
Here's photo of the type of bee your dealing with.

Let the pro's handle it, if it can't wait.