Generator in Class C Rental

4k Genset is actually small and tells me your rental is 30 amp. Not sure what the temps will be when/where you travel but it sounds like you won't need heavy AC usage. Sounds more like you want to keep the batts charged etc. Most big box rental companies don't have TV's so I am really not sure what you will use all this power for. Your water heater is LP, heater LP, stove Lp, refer LP, etc. Your AC will need electric, and your batts will need to be charged. Even if you ran it the prescribed 4 hours a day, I would bet that will burn less than 3 gals of fuel. 3 gals over 11 days is 33 gals. At USD $2.50/gal you will spend $82 USD. You would have to actually run the onboard generator 120 hours, or 10 hours a day to equate to the cost of your generator rental. And your generator rental also needs fuel. Add to that, your onboard generator uses the motorhome's gas tank. How are you going to transport all that fuel for the Honda generator? in summary, it's just plain easier and cheaper to use your onboard generator. That's why it's there. The ONLY variable is what they will charge you if you go over the generator usage limit. Probably something like $.50/hour - unless the $100 fee is unlimited usage. Then it's a no brainer.

On Edit;
I don't now where you are camping but you mention dry camping in campgrounds - unless I mis-read that. Is there a reason you aren't camping with electric hookups? And you will need hookups eventually if anything to dump your tanks and replenish water and probably LP. Is the cost of hookups at a CG more than the money spent on gen usage? Not sure I fully understood the dynamics of where you are staying.