Birth mother is trying to turn over adoption what should we do?

My mother was going to adopt a baby girl from a twenty three year old women. The baby had not been born when this was decided. In the hospital, the birth mom decided she wanted to keep the baby after letting my mom think she was going to get the baby for 9 months! (Makes me angry) So the birth mother kept the child for six weeks and then called my mom and says, "I don't love this baby and I don't want to care for it anymore I am giving up my rights to you." So the birth mom signs off her rights and my mother and I now have a wonderful two month old, Lilah. After about two weeks, the birth mother started calling asking for her child and claiming "she made a big mistake." The father who is residing in Japan says he will sign off his rights but he has yet to do so. He does not want the baby but we are afraid the birth mom will persuade the dad to give the baby to her. The birth mom calls many times a day, leaving voice-mails trying to make my mom feel like dirt. It's getting to the point where we feel somehow we will loose the baby. What should we do?