OP, I see from your name and the number of posts you have that you have been on the DISboards a LONG time, so you had to realize what was going to happen when you posted this. Not everyone reads the entire thread, not everyone understands what you mean, and many people jump on one or two things and just go to town on it, over and over. It would have been nice if people could have seen that you were asking for help and advice in this situation, instead of dumping on you repeatedly, poster after poster, to tell you what a terrible person you and mama are, how baby is being abused, etc. I'm really sorry about that, but you had to know it was going to happen. This happens all the time with "hot button" topics here; lots of bashing, minimal true advice given.
I don't know what you have tried and what's not worked, but it's hard when a child continues to cry, regardless of what you try. I had a daughter like that myself- she wouldn't even stay with her father, just cried and cried while I was gone. She didn't like to sleep at night, either, and would cry and cry when we put her down for the night. I went with my instincts, picked her up, rocked her, etc. Guess what? My pediatrician recommended letting her cry it out at night until she'd fall asleep, said that babies get it eventually and they'll be fine, they won't learn to self-soothe if you go in to them, etc. I responded just awhile ago to a thread, saying that DD would stand at the door and cry whenever I left the house, how we'd tried everything, and many many of the good folks here on the DISboard told me that by not letting her cry it out, I was setting DD up to be overly dependent on me, that she'd have a lifetime of woe because of her dependence on me, maybe I needed to learn to let go, etc. We figured it out at the time, and DD has grown up happy and healthy.
One thing I noticed was that the only person DD would stay with, without crying, was my sister, who sounds exactly like me. Maybe you could get the mama to make a recording of her own voice, singing some of baby's favorite songs or reading to her. When the crying gets bad, you could hold baby and play the tape. Maybe that'd help soothe her.
I know people are all hot and bothered about this

, but there are as many different opinions on how to raise a child as there are posters. I feel badly for this baby you watch, NOT because I believe you are abusing her, but because she is obviously sad and distressed. I think it's good that you realize your experience with young children is limited and are trying to find out ways to help her. When I think of the number of children I see who are bruised, burned, and broken by their caregivers, I have a hard time getting worked up over a child being put in a crib, checked on repeatedly, taken out to play at intervals (READ THE POSTS PEOPLE), in a situation where someone is honestly asking for help. I would say, make sure the mama knows how her baby is reacting, how you are managing it, and ask if she has suggestions/ideas. Maybe you can work on it together to see if you can come to some resolution.
And for the record, I think it's FAR creepier to stalk/hunt down a person's posting history than for a person to refer to someone in the story as "mama."