Who are the insurance companies? Most times, they just duke it out and you talk to your insurance company.
Ha! yeah, right.
In my experience, your insurance considers it not their problem, they have no reason to be involved.
The EXCEPTION to this is IF you have additional collision insurance, then they will pay you out under that policy, and they then go after the other company.
the problem is, even then you have to deal w/ an insurance adjuster who has no motivation to give you a penny more than he is obligated to.
For the record, I've seen this shake out many different ways. Almost a crapshoot. I had to haggle like hell once to get a good value on an old Cherokee, but then on another occasion was given way more than expected for a newer Toyota Matrix... then recently when my nephew was hit in his $500 POS escort, they gave them $1800... so you never know.
IMO unless there is a lot more to it than just a car value, or it is really a lot of money, the cost of a lawyer is going to be challenging to justify from what the difference would be.
In NC you have the right to argue and don't have to accept their offer.
One important tip - if you haven't already, demand they provide a rental. They HAVE TO. Even if you don't really need it, get it. The alternative is to ask that they pay YOU the cost of the rental for each day. They can do that too.
The point is, this gives them more incentive to close the case quickly, b/c every day costs them money. But you don't have to accept/close out until you are happy w/ the payout. So this gives you a bargaining chip.