How to get rid of a dog humanely?

It sounds like your poor dog is stressed out, some reasons might be due to the new changes. That is part of the chihuahua breed. You shouldn't give up on her, but it sounds like you and your family don't know how to handle a high strung dog. Caesar Milan has MANY episodes on how to deal with that type of dog and changing the environment to help the animal which will eventually help your life be less stressful. If you and your family aren't willing to put in that time for a 'family member' then I would say that dog could be better off with another home than sitting in a room alone all day. It would be a long road for her either way.