I agree with Rex about not removing the paneling. The manufactures of coaches just use double sided stick tape for most all mirror installations straight onto the wallboard. Be sure to clean the surface; denature alcohol is good. Also most mirrors I have seen are only 1/8" thick. You could have a glass company provide this for you and you may even want to consider a beveled edge mirror.
Good luck and keep us posted.
Mike, RVIA & RVSA Certified Master RV Technician
Amy, Dr. Assistant - Roxie & Mei Ling, four legs each
2000 Gulf Stream Scenic Cruiser 450 hp & 1330# torque
06 Saturn Vue, 06 Chevy Z71 4x4 & 2014 Corvette Z51 M7