Car totalled, Ins. won't pay

What is the name of your state? Oklahoma

I was in an accident and my car was totalled. I have full coverage ins. including rental car allowance for up to $500. The Ins. Company offered me $3100 for my car, which is less than the "low retail value" according to the NADA. My car was in good condition which puts the value anywhere between $4675 and $5500. Don't they have to pay according to the NADA values? What are the laws governing this?

To add insult, they are now refusing to continue paying the tow lot for storage and the car rental because they say, "they've made an offer, and I've refused therefore they don't have to pay." Is that legal??!! It has only been 2 wks since the accident. I've had the rental car for 1 week.

What should I do?? thank you for your help.

You will have to pay the difference between what is owed and what your insurance company deems appropriate for payout. They will probably include the rental fee after you agree with their terms. Just ask them if you accept their terms if a rental will be included since you are paying for it.
This happens all the time. The minute you drive your car off the lot it loses value. You might believe your car is worth more, but can you take the time, money and effort to argue with an insurance company?
I am not an Attorney, but have gone through the same thing with a wreck. Our van was totaled and we had to pay the balance which was about $3,000. We however were thankful that the insurance company gave us as much as they did. It had MANY miles.