If you take your vehicle to a body shop that charges more for labor rate than what insurance is willing to pay and you have full coverage on vehicle how do you get your insurance to pay up?

No Insurer is required to pay unreasonable rates for repair. Insurers know what the average cost is for various vehicle repairs. There is a high end and a low end. This is why you should always get an estimate of the repair costs first and have the repair shop contact your insurer before you authorize the repairs.