I think it was missing this CRUCIAL horror story element

So let's look at the horror/terror genre. It is an exploration of fear. If you have a baby, your fear isn't just that someone would want to hurt your baby, but that they would want to kidnap your baby.

I felt that this element was hardly played. The villain should have had dialogue. "I want my baby back! Give me my baby!"

We could have had the police in this movie, reassuring them that they would keep them safe, that nobody was going to take her baby, that it was all post-natal stress.

I think that had this been explored, the shots of the crazy lady with the baby would have been more powerful. Maybe a shot of her looking outside and seeing her, and she is swaying with the baby and has a devilish smile. Perhaps there could have been a lake and it's night, and she starts to walk into the lake with the baby (drowning is a big fear for parents).

So the writers needed to do their homework and figure out what are the fears that parents have about babies and exploit them. A baby in a cart at the top of the stairs? I'm sure that's not high on their fear list. It should be things that they themselves worry about (perhaps a stroller at the top of the stairs.)