Sunburn happens, and no one else is likely to take as good care of your daughter as you would yourself. You may have requested that the nursery school reapply the suntan lotion, but the legal issue would be were they aware of any special circumstances compelling application of sunscreen and were they sufficiently negligent by not reapplying the suntan lotion and/or leaving her out for an unreasonably long time in bright sun.As a practical matter it would have to be one major sunburn requiring meaningful medical treatment and perhaps resulting in permanent damage to make it worth while for any successful lawyer to be interested in the case.Without a lawyer the nursery school would not pay, and its insurance company would defend and if there was any recovery that part of it not needed for medical and legal expenses would be put in an account for safekeeping for your daughter until she turns 18.