Going back to work

Depends on how long he's expecting the child to be in daycare. When would he be having a relationship with his child? Personally why would it be 50/50 cost...you aren't using it? How old is the child

Does he normally sleep all day? He can't expect you to parent overnight and work in the day if he won't pick up the day whilst you're at work. I'd understand mornings at day care so he can sleep after his shift but I'd definitely be expecting him to pick up at lunchtimes and actually be present in his kids life.

Without details on the man, I think it's reasonable to an extent because if he works all night then has the baby all day then at what point is he supposed to sleep? Shift work is hard, it can legit take years off your life. And I do believe childcare costs should be 50/50 in this instance because it's both of your child that needs the care. If a dad was working in the day and the mum overnight and he told her he wasn't paying towards childcare for her to get a rest in the day there would be UPROAR on here. Most babies sleep more at night if not now then eventually she will. In the meantime he can do more on his off days to get you some rest if you're struggling overnight.

HOWEVER there are compromises he should be willing to make. E.g just the morning so he can sleep then he has her for the afternoon, if he's usually up after lunch time that's the perfect time to go pick her up. This will reduce costs for you both and less day care time for your child as well.