Wow. I had the same question the other day and almost felt like I was reading my own request. My daughter, also 2 years old, is in the exact same situation. She has been at her new in-home daycare for a little while now and this week has been the best by far. She hasn't clinged to me screaming as I walk out the door for the past 2 days! I tried a few differnt things and they may or may not work, but it is always worth a try. I had her take her favorite blanket, something of mine, a little picture book that had pics of myself, my husband, her brother and aunts, uncles any family member that she is close with. My husband and I have also been taking turns calling her in the morning.
The new provider was noticing that she was just having the issues in the morning, but after her nap she was doing good. I started putting her to bed earlier. She has allergies, and was taking benedryl in the morning which I knew would also be making her sleepy so I stopped giving that to her in the morning as well. My husband and I are not above bribing either. We preped her this weekend and told her that she would have a suprise if she didn't cry in the mornings when she was dropped off. I don't know if any of the things we tried was what worked, or she just got used to the kids and the new provider. I think that it lessend my feelings of guilt & anxiety knowing that I was trying everything that I could to make it better for her.
I did read that children experience separation anxiety around the age of 2, but couldn't find any good ideas for this stage. Good Luck to you and if I have any responses to my question, I will send them on to you.
C.