I think in this situation you have two choices. A) Find a new home for the dog or B) since you and your mother were the ones to originally get the dog, ONE or BOTH of you need to step up and do obedience classes to have it fit into the existing pack/human structure.
Has your dad become attached to the dog at all or do they just merely exist together but your dad doesn't show any interest? Even though this is a family dog, he might just be unwilling to have it take the place of the dog he lost and therefore, has no interest in being its keeper.
Oh my, the OP removed her post. I am not sure how you can see where it is going with one post. Well, I suppose since they did not say what you wanted to hear.
My first thought was that I am not sure you know what a really well behaved dog is if you think it is OK for your mother to take a dog everywhere that barks at all strangers (what you said). I highly doubt one instance of the dog being taken away from your mother is the cause of the dogs barking.
On your father's dog I totally agree with Vaguero.