D.B.
Your are right, the problem is mom is there. I think your daughter would do fine if she was one on one with this baby. If mom appears every time the baby cries, the baby will continue to cry. Maybe your daughter could take the baby out, go for walks or something.
She needs to talk to this mom and they need to agree that mom will not appear when the baby cries. The baby needs to think that mom is gone. Maybe mom could study someplace else? Maybe she should be the one to leave, go to the library or something. This baby will keep crying if mom keeps appearing... that's the bottom line.