Just make sure the bolt diameter isn't a large fraction of the size of the metal brace. For a 10 lb TV, only mounted when stopped, I wouldn't think the fasteners would weaken the floor support, unless you're mounting it with 1/2" bolts.
Rather than drill holes in the RV and have a permanent mount on the exterior, you might think of a tripod or even a camp table to mount the TV, it would give flexibility to be able to move it away from that spot on the RV side.
Bob & Donna
'98 Gulf Stream Sun Voyager DP being pushed by a '00 Beetle TDI