I'd go ahead and get whatever starting battery your vehicle requires. Then, wire in a 12V charge line from your Motorhome to the Tahoe so this won't be a problem anymore with the new battery.
That way, you won't be using your vehicle's starting battery like a deep cycle battery, and ultimately shortening its lifespan as a result. Cars really need a starting battery, not a deep cycle. If you use a starting battery like a deep cycle and deplete it low regularly....Welll, you shorten its lifespan and end up in the spot you're in now.
Find a way to run a charge line to your Tahoe, is my vote.