I would be taking pictures of what happened to her. Just in case you never know.
I would go in and have a conversation with the daycare owner. That is not right. Your daughter could have and ALMOST was seriously hurt! Her eye got infected. That is serious enough as is. I would go in firm and tell them all this and ask them how its possible to have something go almost through her eyelid and to her eye from "falling on a pile of sticks"??? It DOESNT thats why!
I would see what they have to say for themselves. They obviously arent keeping a close eye on the children and who knows what could happen.
I wouldnt pay them the full two weeks if it were me that is ridiculous. Does it say in the contract that you have to call a parent or guardian if ANY injury occurs? If it DOES then I would tell them I am not paying for two weeks. If they throw a fit and say that you signed a contract, I would simply tell them that yes you did but they also said they would call you.
Your daughter did not simply fall down, she has multiple injuries that are not just small scrapes. At the very most I would only pay them one week, cut my losses, they cut theirs.
Because honestly, they are lucky that you are not considering suing them!!
Glad your daughter is healing well, and I hope you find her a better daycare. I feel bad for the kids who have to stay there and the unknowing parents.