I would say that is normal. DD's been going to daycare since she was 5 months old, but even though she is used to it and is quite happy to be there (to the point of getting mad when there is a holiday and she can't go to school like normal), around when she turned 3 we had some times where she didn't want to leave when I came to pick her up. Usually it is just that she's having a good time playing her friends and doesn't want to leave yet. I've noticed it was more of a problem when I got there early and she was one of the first kids to get picked up rather than in the middle of the pack or toward the end of the group of kids getting picked up. So, sometimes I've hung out at daycare an extra 10 minutes or so while she played a bit more or finished an art project and it gave me a chance to ask the teachers some extra questions about how she's doing or whatever rather than our usual fairly quick pick-ups.
Give her some time - she hasn't been going to daycare very long and it's a big adjustment when she was used to just Grandma and being the only kid all day.
As a side note, we also went through the doing or saying the opposite of what she knew we wanted just to be defiant. I swear if I said the sky was blue she'd say No it isn't. That's when we as parents get to have fun with the reverse psychology! i.e. "I don't want you to pick up your toys - just leave them all over the floor." She'd pick them all up and put them away. Lol!
The I don't love you thing - it hurts when they say it, but try not to take it personally. She's testing for a reaction. My DD said that too - I just looked at her and said "Ouch! That hurts my feelings. Well, I love you, and I'm not going anywhere, so you better get used to it." and then just dropped the subject. Later that night she said she loved me and gave me a hug.
Hang in there - I think 3 was harder than 2.
Holly (31) DH (38) DD (3-born 11/16/07). Full-time working Mom, Wife, Library Board President, Chef, Chauffer, Maid, Toy Assembler and Repair Technician, and Chief Boo-Boo Kisser.