I think this is normal. My daughter is 27 months. She told me yesterday that WE HAVE TO TAKE CASSIDY BACK TO HER MOMMY (Since she never picked her up from the hospital). She hasn't been visibly mean to the baby but she has declared her daddy her "Favorite Daddy" and wants to spend every hour with him.
Also, we've been sending Kennedy to daycare. She actually started going to a more structured setting (was with my aunt until new year) and loves going to "school". I, like others who've posted, needed her to have this routine down before I return to work. Also, she enjoys going and her friends are there. I pick her up earlier than when I will when I return to work. She is a handful and would be so bored at home with me and the baby.
I understand that this adjustment to new baby takes time. I vividly recall my brother coming home with my mom (I was also 27 months). Mom said I picked him up and tried to drop him. I do think the 2-3 year difference is ideal in the end. My brother and I are very very close and somewhere during my elementary school years became one of my best friends.