E.W.
T.
My son was a little over 2.5 yrs when my daughter was born (via c-section). Here's what I would recommend:
1) you will not be able to pick up your daughter for 6 weeks after the surgery...so start prepping her for that now (so she doesn't feel shunted). I told my son that I would have "ouchies" after the baby was born and wouldn't be able to pick him up...and let him know that that made me sad. I told him that I would still be able to hug and cuddle him and promised that I'd do a lot of that.
2) involve your daughter in as much as possible so she feels part of things....and feels like she's helping. It was my son's decision to give the baby the crib (which was previously his toddler bed) after we got him a big boy bed. I got the bed and actually put it up in the living room so that he could get used to the idea, told him what it was, and eventually he asked if he could sleep in it. So, we then moved the bed into his room...but kept the crib in there too (so that if he didn't like the big boy bed, he could go back to the crib). After a few nights in his big boy bed, I casually commented that he'd have more room for playing if the crib wasn't there and wondered out loud what we could do with it. He then said we should give it to the baby. This is just an example. But, basically, you don't want your daughter to feel like all of her stuff is being taken from her and given to the baby. If you can make it feel like her decision - it will go much more smoothly.
3) I love that your grandma is going to help out. For daycare....make sure that you prep your daughter for this change now...and make it a special treat. Maybe something like "with the new baby coming, Grandma wants to make sure she still has some alone time with you...so she has asked to take you to daycare and pick you up". I second the opinion of others about having your daughter stay at grandma's. As you mention, you don't want her to feel shipped off to grandma's. Is there anyway grandma can stay with you? If not, then make sure the idea is presented to your daughter early (so she knows what to expect) and make it feel like this is a very special treat for her.
If your daughter is already being mean to you, then she's already likely feeling the effects of the change. If you can, take some time and just hang out with her and make sure she clearly understands what will be going on in a few weeks. And when she really gets under your skin, just remember, all she wants is to be loved....and she doesn't understand why you want another baby around. Anything you can do to help her feel more secure will greatly ease the transition.
Hope this helps!