M.P.
Your daughter is acting this way because she does need something. What is difficult is to figure out what it is.
First, I'd say the "honeymoon" period is over at the new daycare. We all are good at the beginning. I adopted my daughter when she was 7. For the first few weeks she put her toys away without being asked. It went down hill from there. :)
It sounds like she has only been in one daycare previous to this one. So her world is different and kids freqeuntly have difficulty adjusting to a new place. She is making sure everyone knows that that the binkie, blankie, and sippy cup are hers. At this age they are beginning to realize that they are individuals and certain things are theirs.
She has come from a situation in which she had only 1 other child to which she needed to relate. How old are the other 2 kids in this daycare? Keep in mind that at 2 kids usually play side by side most of the time and not actually with each other. Have the workers shown your daughter some of the toys and got her involved with them away from the other kids but close to the worker?
Another thing the workers can do is to ask her to help them. Experienced ones have figured out all sorts of ways to involve kids in such a way that they feel safe and loved.
Since this is a new daycare they may not know how to handle this. I think it would help if they told the other child that this belongs to your daughter's name before your daughter becomes upset. Does your daughter have a cubby or a drawer where she can put her things? That might help.
Also, how is the one worker that she clings to dealing with it? If she is pushing her away either physically or emotionally this will cause your daughter to cling even more. My grandson's in home daycare sometimes has as many as 6 baby's and children. My grandson had difficulty adjusting. Eva held him or any child that wanted to be held. If her lap was full she'd tell the one who was on her lap to go get or go do somthing and add that it was now so and so's turn, reassuring them that they could sit on her lap later.
I think that if this worker can hold and reassure your daughter that your daughter will more quickly adjust and be that happpy child again then if they're trying to teach her to be independent.
Also, she is most likely not feeling so well. It takes awhile to recover energy after an illness. Did she stay with you or with someone else while she was ill? If so going back to this one is another change in her world.
Does she know you're pregnant, that she's going to have a little brother or sister? This is a big adjustment too. At 2, kids don't have the words to ask questions or tell how they're feeling. They cling instead.
A more subtle reason may be that your daughter is frightened of the other worker or of another child. What is the demanor of the other worker. Actually what is the demeanor of both workers and does the space give children a sense of security? Everything may look OK to you but it may not be to your little girl. Sometimes babies, toddlers, and kids feel differently about the same people with whom we're comfortable. If possible stay with her at the home for a short while. Even 10 or 15 minutes may help you get a clue. If possible drop back in later, unannounced, and quietly watch.
One way to find out how kids are feeling is to tell them a story about a little girl similar to them in similar circumstances and pause to ask a question, such as how would you feel if you were this little girl? What do you think this little girl should do? Your daughter may be too young for this to work in getting answers from her but it will at the very least let her know that she's not the only one with this sort of situation. Make the ending a happy one and pass along one hint towards how to feel safer.
As to the other child saying she doesn't want to come back, I wouldn't worry about that. These words are said over and over. "I don't like you!" "Go away!" "I'm not coming here tomorrow. You're mean!" "I hate you!" Those sort of things. The best way to handle those is to be sympathetic for the child but know that tomorrow or even 5 minutes later they may be the best of friends.
How did the workers handle the situation when the little girl said she didn't want to come back? How did her mother handle it?
If the workers are putting pressure on you to change your little girl's behavior, I think this is not the right place for her. An experienced worker would either know how to help your daughter or would be willing to try different ways to find a way to help her. The more your daughter's feelings are validated the quicker she'll get past this.