Is the TV the one that came installed or one you have added? The installed TV might have an interlock that prevents it from operating when driving because it's in the driver's view.
If the TV is not within the driver's view, it would be legal to operate. If it's a 12 v TV, you could install a 12 v outlet to power it. Don't piggy-back the 12v from a light circuit, run a dedicated wire from the fuse block with a fuse in the wire to the outlet. The ground can be connected to any grounded part of the RV.
I added speakers under the dashboard in front of our RV and installed a DPDT switch on the dashboard that cuts out the rear speakers and sends the sound to the dash speakers. You could do a similar wiring job for what you propose. The TV audio might not be powerful enough to power the roof speakers, you might have to wire a small amplifier into the audio out of the TV.
To power an outlet in the kitchen for 120 v AC you'll need an inverter. They change 12v DC to 120 v AC. What do you wish to power? If it's the microwave, coffee maker, toaster, or other high wattage item it will require a permanently wired properly sized inverter. If it's just a phone charger or the like a smaller inverter than can be plugged in a 12v power outlet can do the job.
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Bob & Donna
'98 Gulf Stream Sun Voyager DP being pushed by a '00 Beetle TDI
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