How are ovens and range tops connected?

On a typical RV oven with a stove-top, yes, the two units operate independantly but separating the two is nearly impossible due to the design.
Under the stove-top is a manifold that the burner gas valves are connected to and also attached to this manifold is the thermostat/control for the oven. If one were to go through the work cutting the two apart, you would then need to have a new manifold for the oven by itself and would need to remove the thermostat from the original manifold and plug that outlet.

I correct my first statement where I said "nearly" impossible and change that to impossible and not worth the time, money and danger of modifying an existing gas system design.

The cutting board cover is a good solution, retaining the stove burners in the process. I've seen extensions for counters that rest against the counters end and flip up when needed.

Peg Leg wrote:
We thought the smell was something burning in the oven before realizing your thinking process was just clearing out the cobwebs. You may as well fess up with ideas. Now everyone that doesn't use the oven is gonna have light bulbs going off. If you don't steer us down a path we could have a runaway power surge.

I see. :)

Well, the thought was that often small Class C's don't have enough counter space, and wouldn't it be nice to swap a 17" wide 2 burner range in place of the standard 3 burner range, including a new counter top in the deal. So far we have dealt with the issue with a wood cutting board/ range cover. And that's likely to be the long term solution as well, considering what I've read above.

We thought the smell was something burning in the oven before realizing your thinking process was just clearing out the cobwebs. You may as well fess up with ideas. Now everyone that doesn't use the oven is gonna have light bulbs going off. If you don't steer us down a path we could have a runaway power surge.

Push on the two front corners of stove top to release it and then lift up.......
one unit. Stove top burners are assembled on the top of oven section.

The stovetop and oven on a typical RV range operate independently and many can be separated as you describe.

Degree of difficulty depends on the original design- some consist of two units, stovetop being simply screwed to the top of the oven part. Others may require cutting the sidewalls at the appropriate joint where the two parts meet.

There was a thread here recently posted by someone that did this mod- I could be mistaken, but I think they did so in order to install an electric convection oven in place of the gas oven.

Usually the Oven/Range is one unit like in a house. You can get just a range top and replace the oven area with cabinet drawers, and replace the Microwave with a micro/convection if you want.