Look at the socket where the TV is plugged into. It will have normal romex wires and two separate wires that carry 12v DC power. Those DC wires are connected to the ign. switch and supply a 12v signal that kills AC power when ign. is turned on (moving down hiway).
Cut or disconnect the 12v wires to the socket so it can not receive the signal and the socket will remain powered when ign. is on. Now you will be able to turn on inverter and have ac power when the coach is in motion.
2015 Jayco Precept 35UN
Towing JEEP TJ with Roadmaster plates and bar w/Blue Ox Patriot brake
an Aluma low bed trailer with HD Road King and/or Polaris RZR onboard