J.S.
I've been a mom and preschool teacher a long time so here is my 2 cents.
2 1/2 is on the young side for preschool. Kids do better socially, emotionally and academically when they are an older 3, young 4. 2's aren't interested in playing with others-it's till all about me, what I want and who will give it to me or let me take it. =) At her age, she engages in Parallel play which is playing with her own toys next to a child playing with another set of toys. There is no cooperative or imaginative play between the two children. Little socialization actually takes place at this age.
Please be aware that biting is common between 2's as well as tons of germs since a lot of mouth sensory exploration is done, so she could get sick a lot.
That said, the behavior you are describing is completley appropriate for her situation. The first day of school, the children do not have a full understanding of what is happening. They think it is play time and when they are done in a little bit, mom will be there to take them home. Then comes the realization of being left with strangers in a unfamiliar environment. Returning on subsequent days reminds her that she was left before she had to stay until you come to get her. Honestly, very frightening for a little one. How long does she attend. A couple hours or all day.
My best mommy advice is to keep her home with you longer. She has a long school life ahead of her. It isn't necessary to send her to preschool now. You are your child's first and best teacher. There is so much to be done at home learning wise and so much more gained from family playgroups.
Should you choose to keep her in preschool, my best teacher advice is to give her a kiss/hug good-bye, tell her you are leaving and when you will return (after lunch, nap, etc.). Keeping it quick is best, no matter how much she cries. The more you stay when she cries, the more she will cry. Do not ever leave by sneaking out. This causes fear and mistrust.
Working in preschools, I used to think it was best for kids. But now that I'm a mom and see more and more kids left to teachers, I realize what I missed out on with my own kids even when I was "just down the hall from their classroom." I wish so much that I didn't miss out on so many things.