You'd better consult with a Personal Injury lawyer first. PI lawyers take cases which the potential defendants have money or insurance. In your case, the kindgarden may have insurance.
If there is no money, it comes done to justice, i.e. let the babysitter pay for what she could have done wrong or had done wrong. However, unless the district attorney finds there is a case, you may not get what you want.
In this case, consult a criminal defense attorney to see whether there is any proble cause for charging the babysitter.
Of course, if you could, try to find the criminal liability first. The standard is higher than a civil case. If the babysitter was found guilty, then you could file subsequent civil action againt her. Proof of liablity would be easier.
i feel sorry for your loss. But sometimes the law views things differently.