Maybe the Daycare she goes to, she doesn't like it. Maybe something there, the environment or the other kids are a negative mix. ASK your child about it... she's 4 years old and can certainly express herself or "explain" in her own words for her age.
Talk about it with her.
Sometimes, a child may just be slow to adjust, sometimes they have reasons they don't like their daycare venue. Explore it and investigate that. Ask the Daycare provider about she behaves after you leave... are there any problems? Are their any problems with other kids and your child? Is there any teasing or bullying? (yes, at this age that can happen already. My girl was treated this way by a classmate Preschool at 4 years old). ASK about it...
Or maybe it's just her personality. My sister for example, was that way, and anytime there was something "new" to adjust to... she cried and clung to my mother. Even as an "adult" she had a hard time adjusting to new things. But, all is better now finally. She has become more flexible as a person. LOL.
PERHAPS.. .instead of Daycare, put her in a Preschool. Sometimes this can change their feelings/attitude about it. Perhaps she is simply going through growing pains... and "becoming" a "big-girl." It can be scary for some children.
She won't "hate" you... but she is obviously having trouble with something... adjustment, letting go, feeling all alone, being in a group environment, new expectations and routines etc. Does she have "friends" at Daycare? Or does she socialize well? Or is she more of a loner? Personality can play a part in it, and if they have developed friends.
talk and chat with her. Don't judge her... but see what she says. What is the Daycare provider like? Are they nurturing or cold and authoritarian? Maybe your girl does not like the way they manage the kids or "discipline" or handle the kids? It could be anything. Or, she is just needing more time and comforting to adjust.
It will pass. And before you know it, she will be all grown up! Good luck, I know it's not easy. Sometimes, my girl at that age, would act like that too...but it was at times when she was "stressed" (yes, kids can get stressed out too)... and when something new was happening (like me being pregnant at the time with my 2nd baby, and she was starting Preschool then too etc.) But I always talked about it with her... since that is her personality. And it made her feel better.
Perhaps, give your girl something "special" of yours, to take to Daycare with her... a photo, a special necklace etc. There is also a book called "The Kissing Hand" which is a classic... read it to her. That's what I did to prep my girl. It is all about going to "school" and having a special "kiss" to take with her.
Take care, hope it helps,
~Susan