I understand your goal is to get some sleep, not to torture yourself and the kid, right?
Here is the stories to compare:
Mom#1: At bed time puts her baby in a crib, attemps to free herself from child grabbing her arms and sobbing, walkes out of the room, closes the door. Baby escalates her sobbing, mom hears everything but refuses to budge. That goes on for 45 min.
Mom is a nervous wreak from listening to all that crying, hears the sounds of vomiting from the room, enters the room, cleans and changes the baby, remouves and changes the bedding. That takes 20 min.
Baby calmes down somewhat, because mom is here and the baby thinks she is here to stay. Mom leaves the room again, baby picks up the crying fit. Crying for 60 min, falls asleep from exaustion.
Mom falls asleep 15 min later because she is exausted too but feels really bad about all that crying and not exactly sure that baby calmed down for good.
2.5 hours later, baby wakes up and realises it's all alone, starts crying again, louder this time because it had some rest...Mom cannot sleep, listens to crying but refuses to give in and go to see the baby. Crying goes on and on for 50 min. Mom realises that baby may be hungry (because it vomited earlier) goes in, feeds the bay, baby falls asleep in mom's arms. Feeding took 20 min. The moment mom wants to lay the child down, it starts to cry... Mom#1 exausted by all this desides "you will sleep alone, I need some rest too!" Leaved the baby alone, until she hers the vomiting sound 30 min later....Cleaning and changing routine all over again....takes 20 min....then crying again for 1 hour before falling asleep, exausted mom falls asleep 10 min after the baby.....In 3 hours... mom hears the loud wail, looks at her bedside clock - it is morning. She is beyound exausted! Total time spent in "childcare" all night- 5 hours!
Mom#2: Lays in bed next to baby, talking or singing, baby nestles against the mom and asleep in 20 min. Mom gently puts the baby into her own bed, baby wakes up and starts to protest. Mom hugs the baby and rocks her a little bit more, to show the baby it is safe, she is there. Baby drifts off to sleep, mom waits a bit and put the baby in her bed again. This time the baby is deeply asleep and stays in bed. That takes 10 min, mom gets in her bed and asleep immediately because she know that her baby is safe asleep and she is not worked up with any negative emotions. Baby wakes up in a middle of the night, mom tries to comfort her by petting her back (the crib is next to bed, so mom does not have to get up), baby is fussy, mom picks her up immediately, not letting her get too awake and scared. Baby calmes down fast in mother's arms, goes back to sleep. The whole insident takes about 10 min, mom goes back to sleep in 5 min, bacause she never was fully awake to begin with. Baby sleeps till morning and wakes up at the same time with the baby and Mom #1. Mom #2 spent 45 min doing "childcare".
Deside for yourself. Patience and love can do wonders. And remember you can only change yourself, you cannot change another person, no matter how hard you try or how small that person may be.....
Good luck.