As you say, a longer wheelbase vehicle would likely be more stable. However, you might not want to give up on the Tahoe without some more thought and tinkering.
Are you using a sway control device in addition to the weight equalizing hitch? Depending on the hitch, this may be a separate device from the weight distributing hitch, but is probably essential for your set up.
A trailer is going to change the way any vehicle handles. I think a first order of business is to try and figure out if the tow package is actually unstable or if it is an issue of just getting used to it. You might consider having a person experienced in towing drive the unit to get more input. Also, note that the tires on your RV are likely rated not to exceed 65 miles per hour at the rated pressure, so speeds higher than that would not be recommended.
You could research and post additional information that might help others on this site give input on your issue:
1. How heavy is the Tahoe itself loaded?
2. What is the air pressure in the Tahoe and trailer tires?
3. Does the trailer seem to sit level when hitched to the Tahoe?
4. What it the type and tow rating of the weight distributing hitch?
5. What type of anti- sway device is being used?
2012 Chevy Silverado 1500 with factory brake control
Equal-i-zer 600/6000 hitch