I wouldn't listen to your attorney.
In NC insurance is only required by the NCP if it is available through employment. He's not getting insurance through work correct? If he has a private policy and does not have insurance through work then he isn't required to put her on the policy.
This is what the guidelines say about insurance..
Health Insurance and Health Care Costs
Top
The amount that is, or will be, paid by a parent for health (medical, or medical and dental) insurance for the children for whom support is being determined is added to the basic child support obligation and prorated between the parents based on their respective incomes. Payments that are made by a parent's employer for health insurance and are not deducted from the parent's wages are not included. When a child for whom support is being determined is covered by a family policy, only the health insurance premium actually attributable to that child is added. If this amount is not available or cannot be verified, the total cost of the premium is divided by the total number of persons covered by the policy and then multiplied by the number of covered children for whom support is being determined.
The court may order that uninsured medical or dental expenses in excess of $250 per year or other uninsured health care costs (including reasonable and necessary costs related to orthodontia, dental care, asthma treatments, physical therapy, treatment of chronic health problems, and counseling or psychiatric therapy for diagnosed mental disorders) be paid by the parents in proportion to their respective incomes.
The court may order either parent to obtain and maintain health (medical or medical and dental) insurance coverage for a child if it is actually and currently available to the parent at a reasonable cost. Health insurance is considered reasonable in cost if it is employment related or other group health insurance, regardless of delivery mechanism. If health insurance is not actually and currently available to a parent at a reasonable cost at the time the court orders child support, the court may enter an order requiring the parent to obtain and maintain health insurance for a child if and when the parent has access to reasonably-priced health insurance for the child.
https://nddhacts01.dhhs.state.nc.us/home.jsp?TargetScreen=WorkSheet.jsp
This is also a helpful site.
http://info.dhhs.state.nc.us/olm/manuals/dss/cse/man/index.htm
You can ask for anything in court that you want but it doesn't mean you're going to get it and it doesn't mean he's going to follow the court order. There are no gaurantees on anything.
NC does offer NC Health Choice for children. It is state insurance on children and you pay a certain amount every year for each child and a copay but the only way you can get this is if you DON'T qualify for Medicaid. So you can't get it anyway right now because you qualify for Medicaid. In the event you don't then you can ask to be switched to NC Health Choice, but they're supposed to offer it to you if you end up not qualifying for Medicaid.
If it were me, I'd keep her on it just for now and see if I could still put in the paperwork that you would like to obtain private insurance and at such time that you receive it, that you would like to request he pay half. See if that is an option for you because you can always have the order modified later.
Shop around for different insurance rates, although, I've searched and searched and I can't find anything much cheaper than the rate you found for private insurance.
Once you're able to start working, you can try to get a job that has insurance benefits too.