Your best bet is to let a local personal injury lawyer pursue compensation for all damages to family and property. Avvo has a terrific "find a lawyer" tool to locate a top-rated Avvo attorney with a low contingency fee.
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First, I would be skeptical if what an insurance company tells me about coverage.
Second, If there is no coverage you and your family can still recover from your own insurance company for personal injuries if you have personal injury protection and / or uninsured / underinsured motorist coverage. Sounds like you might have full coverage.
You should consult an attorney to see what action should be taken against the negligent party as well as what action, if any, you should take against your own insurance company.
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With all these problems with various insurance companies, you should hire an experienced personal injury lawyer to represent you and your family. You will decrease your stress and maximize your compensation when you have a lawyer representing you.
First, you need to get the accident report from the police. Second you need to take pictures of your vehicle and any visible injuries. Third, you need to consult an attorney that handles auto accident such as yours. Collecting the above information will speed up the process for an attorney to sort through the facts and determine which insurance policies apply to your case. The tactics by the insurance company is common and you need to have some one on your side. A qualified attorney can accomplish this for you.
This answer is intended ONLY to educate the general public about personal injury issues. Every case is different. No client-attorney relationship is created by submitting this answer to the question posed.
All reputable personal injury firms that I know of provide free consultations for personal injury cases. Most will agree that you need to CONSULT WITH A LAWYER. From handling hundreds of similar cases I can tell you with certainty that insurance companies look for excuses to deny liability and avoid payment if possible. Do yourself (and your other family members) a favor and call a good personal injury lawyer.