How do I stop my recently nippy dog?

I have a Beagle- Australian Shepard mix, who has what can best be identified as little-man syndrome. She is EXTREMELY obnoxious about strangers in the house, even if these "strangers" she's met a million times before. She is terrified of children, having had a lot of bad experiences with being kicked and abused, and this causes her to growl at them and not let them come near her. Recently, a next door neighbor came over that she knows well enough, and she nipped him in the back of the leg. Probably a week later, a small girl came over when I wasn't home, and she nipped the poor girl in the hand. Just now, a close friend of mine came over, who tried to reach out and pet her, and though she has also known him for some time, tried to nip him as well. I'm at my wits end, with my mom telling me I need to get rid of her, but I know with her attitude towards strangers she would not be able to be adopted. I should also add that she has been socialized since I first held her in my arms, and used to be able to just fall asleep in anyone's lap, even if she had just met them. She is also an alpha, and since living with my mom, who owns 2 black labs, has become increasingly stressed out. We are know giving them to better homes, because I am about to have a baby, and as they are sweet dogs, we don't have the time or patience to properly train them. The best thing for them is a new home, but for Lexi, the dog in question, I know in my heart that is not the case. PLEASE HELP!!!!