Hey, it's tough doing all the bedtime shifts!! I don't BF so not sure if this will be helpful...do you use a bottle for any feeds or are you EBF? I imagine baby is prob thinking why would I fall asleep with Daddy when I can cuddle up with Mummy and get fed at the same time!
Maybe if you either expressed/formula fed at the last feed when Daddy is doing bedtime? He'll prob still fall asleep whilst drinking a bottle when he's with Daddy.
Also when Daddy is doing bedtime are you near by? I think I remember midwife saying that babies can smell breast milk/Mummy so if he can he's naturally going to want you and not Daddy. I would also say Daddy will prob need a bit of patience/perseverance too before bubba gets the hang of bedtime with Daddy.
Sorry if I'm barking up the wrong tree with things you've already heard/tried xx