I do all the nighttime parenting most of the time because Daniel works a swing shift. Crying in daddy's arms doesn't work here either. I was in a very similar situation before DC was born and it didn't work out until after he came, I actually slept with Lucca the night my labor started and put her to sleep 4 hours after he was born. So I understand how you are feeling
What worked for us was changing how she fell asleep. It was a loooong week because I had a newborn too so I don't suggest waiting until then! I did the "I'll be right back, I have to go get the baby" then I would turn my back to her and tell her she had to lay on that side of me while I nursed the baby. I started taking longer and longer to get the baby and she learned how to go to sleep on her own. Then at night wakeups I started getting up right before she fell asleep, until I would come in, tuck her back under the covers, say goodnight and leave again. It was slow and gradual, but changing how she fell asleep really made a big difference in nighttime sleep.
Eta: there were tears. But I always came when she called me and I didn't let her cry if I could tell she couldn't get over it herself. There's a difference between "I don't like this" and "I need you" tears. She didn't like the changes at first, but then she took ownership of her room and kicked the baby out. I went with the baby and she was happy. Now she generally puts herself to sleep and sleeps all night.