I think this driver should lose his/her job, and that is the likely result if you complain to his/her employer and/or the school. It is even possible that the driver has committed some sort of crime, involving neglect of children in his/her care, and you may want to pursue that with the local District Attorney.
However, I don't think you have a claim for negligence, because such a claim generally requires actual monetary damages. For example, if a driver runs a red light and hits your car, you can sue for negligence and possibleycollect damages for the damage to your car, your medical bills, pain and suffering, etc.; if the same driver runs a red light and misses you, you have no civil claim for negligence, although the driver could potentially still be prosecuted for reckless driving. That could land the driver in jail, but puts no money in your pocket. Fortunately, your daughter is safe and you have no monetary damages.
In rare cases, you can sue for negligent infliction of emotional distress even without monetary damages, but I don't think that you would be able to pursue that claim because you were not in the "zone of danger" for the negligent conduct, although you should check this out with a Delaware lawyer because the elements of such a claim may be different in Delaware than in the jurisdictions in which I practice. If your daughter suffered emotional distress, you may be able to raise a claim on her behalf, but it will be difficult to show that a 5 year old really suffered such distress and, moreover, the litigation could be hard on her as I believe she would have to testify.
All that being said, although I think that your claim is weak, I would think that the bus company would be anxious to avoid bad publicity and might be willing to settle your case for a sum of money even if it thought it would win in court. ...
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