Just my opinions - so take them or leave them.
First off, sounds like she's a typical 3 year old. They go through that stage of 'not liking you', or wanting daddy around instead. You don't need to 'win her back'. Your her mommy, and she will love you no matter what. It's not a popularity contest.
I've found that although I love my daughter, I don't like her as a toddler. She just happens to be a very difficult, independent one that likes to test me very often. Plus, I think we have very different personalities, which doesn't make me love her any less, but makes me feel guilty b/c we don't connect as much as I'd like.
Finally, I think you may be inadvertantly sending the wrong message by sending her to daycare even though you're home. I would think a child would subconciously feel jealous and hurt b/c you're home, and the baby is home, but she gets sent away. She may feel replaced in a way, or that you would rather spend time w/ the baby and send her away.
Which is understandable to me. I mean, sometimes I'd love to send my 3 year old away - lol - and the baby is so new, and growing so fast, plus I'm trying to get to know her. Not to mention, I have no reason to yell at the baby, but I feel like I'm always scolding my toddler. When I hear the scales being tipped that way, I try to be more understanding of her.