@ElizeDavis,
One thing to remember, you must do this with your eyes open. My mothers biological father abandoned my Grandmother when she became pregnant. For years my mother expressed contempt for the man who refused to take care of his family. My Grandmother remarried and her husband became her Dad and my beloved Grandfather. None of my siblings had any interest in learning anything about him, but when my mother had to register for Social Security at 65, they had to obtain her birth certificate. She showed it to me with the name of the of the man who abandoned her. I never had really grasped the fact that she had felt as deeply as she did about him, and I still thing it had a lot to do with how she loved her own children and wondered why he only came back to sign the birth certificate.
I also have a close cousin who was adopted, he tracked down his birth parents and was profoundly disappointed. Those of us who were raised by our parents sometimes don't understand the conflicted feelings of children who find out
someone who should have loved them couldn't be bothered. I hope when or if you get an answer, it will bring some closure for you, and hopefully your Mothers husband was a good father to you. Best of Luck.
PS it should be noted that my mother was born in 1922, society was a little more ridged than it is today