will it make you feel better if i tell you that my then 3-year-old son would try to push his newborn sister out of my arms (no, really) so that he could have my lap?
i agree that this is typical behavior for a toddler who is adjusting to an expanding family and can't have the same kind of attention from you on demand like she used to. i think it's great that she is still going to daycare. kids need routine at this age of development. anytime the dynamics of their circle is changed, it sometimes takes a lot for them to adjust.
i will add that she needs to understand that she does have to do what you say. and i wouldn't look at you enforcing and correcting her behavior as being mean as much as it is you being unyielding in what you expect of her.
i used to read to my kids' preschool classes and it was interesting to see how a group of kids adjusted to a new student or to a student who left for kindergarten. sometimes pure anarchy would erupt! ha! i'm trying to make you laugh. but i'm really serious.