I also wonder if the scene where Ennis is comforting the infant Jennie is a "bookend" to the dozy embrace. There are things that are similar, the way he's rocking her, and perhaps he's murmuring to her. The hand movements are similar. But she is facing towards him, and it would have been awkward the other way around. To me, it is a reminder that we all carry within us the memory of being small, lonely, and vulnerable, and of being held and comforted by a loving parent. Somewhere along the way of growing up we lose that reassuring feeling, only to find it again if/when we meet our true love.
Also, I'm glad some people listened to the lullaby! Isn't it incredible??