Dogs live in packs and their actions come more from the collective thinking of the pack and their role within it than themselves.  If this pack (all the people and the critters in the house) has weak leadership and too much excitement and disarray when someone comes to the door the behavior your seeing in this dog is as it should be for that pack.  
There is much more here that you need to fix than the dogs reply to a person coming to the door.  If your not willing or able to fix all that, including the other dog's response to people at the door, and your leadership then please do consider rehoming her to a pack with strong leadership and good solidly calm other canine examples.  That is first and foremost what she needs.
I know for sure this dog can be rehabilitated and live a very good life where all are safe around her because I have done it with a few, but it's not going to be magical or one step.  All parts of the puzzle will need to be refitted and it will be a long haul.  It will also be however a huge benefit to your life in many ways other than just the 'fixing' of this dog to get the pack set up right. 
To me euthanasia (while an option I admit) is the quick way out that denies you both the life learning that can come from this and the chance to change things that will have a huge impact on your whole life, and that of your family.  This dog has a message for you about the balance in your life, and euthanasia is turning a deaf ear.
All my best in working this out.