In a comp case you are covered because you are an employee. Your children are not employees. Under comp law you are entitled to medical care and part of lost wages. That is it basically.
Any injuries along with any related claims and damages may only be recovered from the workers compensation carrier. If the injury you sustained was on duty, your children may not file a lawsuit against the employer because any claim by them arises out of the injury that was on duty. They may not file a separate claim for personal injury.
Not enough facts are given to respond to your question. However, if your children's alleged claim is related to or dewrived from your personal work-related claim, only you should proceed under your State's worker's compensation laws to seek legal address.
Worker's comp covers medical expenses and time out of work. You cannot sue your employer for negligence. If you have a permanent injury, you may be able to get a "schedule award" which is based on a formula depending on the extent of your disability.
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