Old movie about plane crash with surviving child
I'm trying to remember this old movie (40's maybe early 50's) I believe it was in black and white. It's about a plane crash on a mountain that is difficult to get at with a rescue party. There is a survivor moving that rescurers see through binoculars. It's a child. I think 3 women are called into the rescue center not knowing who is the survivor's true mother. Each woman has a flashback about their baby. The movie ends with one woman getting the child, but I got the feeling that it really wasn't hers. Maybe the real birth mother felt inadequate and she let the other woman think the child would be better off without her.
Could someone help me please?