My son, now 11, had a similar incident when he was 3 years old, at preschool. We were living in Plano, TX & he was a a VERY highly recommended preschool there. He was going down the slide on the playground when another boy came down right behind him. My son fell into the wood chips. He got up, started playing again, and went about his day. I had picked him up about 30 minutes later. He was totally normal. His arm was a little swollen around the elbow the following evening, so I took him to the doctor that night. They took an x-ray - nothing. Fast forward 2 days after the initial trip to the doc & 2 x-rays later at an orthopedic doctor - voila! we have answers. He had a hairline fracture in the bone of his elbow. When I picked him up from school the day of the incident, I could tell he had been crying, and the school told me about it. Funny thing, though, he was crying because he got pushed and got wood chips on his then favorite shirt - NOT because he was hurt. It took me THREE doctors and THREE xrays to find a broken arm. It was his left arm, so he didn't use it as much for daily function (eating, writing, etc.), so it wasn't apparent. Same kid, 18 months earlier - trips over a toy he was carrying, had a hairline fracture in his right arm. He went overnight & a cross country plane ride before he quit using his right arm - come to find out he had a minor hairline fracture in his ulna. I was 2 feet from him & tended to him immediately when he fell.
I agree with a lot of the posters before me, kids can "break" their bones, especially their arms, so so easily - on your watch, your mother's watch or your childcare providers watch, even without you knowing it has happened. If you were at the park, and the same thing happened, you would have cleaned up her lip & unless she was overtly complaining in pain about her arm, would have not even addressed it. Does that make you negligent as a parent? Absolutely not. If she had a bone protruding out of her arm, I have no doubt she would have been on her way to the ER immediately, but these little fractures are SO hard to see sometimes.
At the end of the day, I think you are right to question the process with the provider and the lack of notification, but there are 2 sides to every story. I am not a lawyer, but I would highly discourage your emotional desire to sue this provider over what you deem "negligence." That is such a discretionary term, and incredibly hard to prove. I think you would be appalled what "neglect" is considered in the court and would fall over about how severe that lack of care is. This is not neglect. This is a toddler in a normal environment with other kids, and an injury that, I assure you won't be her last.