Karine,
I'm so sorry that your baby girl has gotten hurt. I know every mother hates to see her child get hurt.
You are correct, biting is a part of childhood for many children. Children who don't have the capacity to communicate frustration or other strong emotions often bite.
My son has bitten other children (and been bitten himself at school- once so badly it broke the skin ) and my daughter has been bitten several times, so I really understand both sides of the issue. I have to tell you that I truly feel any child in any type of daycare setting is susceptible to biting. The only way to have a guarantee that your child won't be bitten is to hire a private nanny.
I have cared for other people's children (off and on) in my home since my oldest son was 10 months old. There were a few times where I didn't actually see the bite happen but could tell with near certainty what had happened based on the locations of the children, the looks on their faces, the body language etc. Also, many two year olds don't know how to lie yet and will readily tell on themselves :-) Has the daycare provider asked the other children what happened?
I have a tiny hunch (could be completely misguided) that the biter might be the granddaughter. Her grandma might be trying to protect her or knows she's backed into a corner because she can't expell her granddaughter for biting.
Two things disturb me about your situation 1. That the provider "has no idea" what happened and 2. That she claims your daughter didn't cry. The latter is the most absurd and in my estimation is probably not true. I believe it is an attempt to minimize the pain your daughter felt in order to keep your reaction at bay.
I strongly suggest that you clearly communicate to the daycare provider what you just told us here. If you have a bad feeling, listen to it. That is your mother's intuition and it is a gift from God. We have to honor that voice inside our head!!
One other thing- when there is a biting incident at my children's school, the parents of both children sign a form (I guess like an icident report). You may want to ask the daycare provider for something like that. It may help her to make sure to see the importance of disclosing to parents how their children were hurt and knowing the full details of how their children were hurt.
I hope that you find some resolution to this problem soon. I can truly feel your frustration from your words and I know what a yucky feeling it can be when you are unsure about something regarding your children.
***Karine: I came back to add that it is NOT illegal for the daycare provider to disclose who bit your child. It may be against a particular provider/facility's policies, but it most certainly is NOT against Florida law. I've included a link to the state laws here: http://www.dcf.state.fl.us/childcare/laws.shtml . Also, you may want to read the section on "direct supervision". You can also call DCF to have them advise you on this situation without having to give the provider's name.