1V drop is about right for the conditions you describe. But 1V is a lot on a 12V system. You'll likely never push that much current because the voltage will drop at the TV battery due to the load on the alternator (the alt ratings are at high rpm, not idle), so you'll wind up down around 12V or less at the trailer battery. That's why we don't trip our 30A trailer charge circuit c/b's when we run 10 AWG wire to the trailer connector. Maybe if you started with a fully charged TV battery, a fully discharged trailer battery, and immediately drove off so that your alternator was putting out its full current.
Please DO install that 30A breaker btw, the closer to the battery the better.