S.J.
One thing that has worked for me is using a bobby. I have 3month old twins and my girls were the same, they only wanted to sleep while being held or on their tummy's. I started putting them on a boppy (on their back) in my bed then eventually moved them into their crib with the boppys. They are sleeping great now all by themselves. I think the bobby helps them feel secure b/c its like they are being held. I'm not sure if they would let you use them in day-care, but it's worth asking. As for mixing up days and nights, I think they eventually grow out of it. Try feeding her right before putting her down at night and sometimes a bath helps. Good luck and congrats!