You need to get a generator that can send all of its rated output into a single 120v outlet. Yours does not, it sends only half the rated output into a single 120v outlet--unless you rewire the head, which sounds like something you wouldn't want to tackle.
There is a lot of good info on the 3000w chinese genset thread concerning that issue with various brands and models.
It does not have a 120/240 switch, but as it has different outlets for 120 and 240, this doesn't strike me as irregular.
This tells me that your generator windings are in series. As I stated in my previous post, this is common among some brands and models of the Chinese generators especially Champion. Your generator may say it is 4000 watt, but you will never be able to use more than half of that in to one 120v circuit (like your RV.) This is because you will only ever utilize one of the two windings in the generator's head.
That method of wiring the generator makes it a poor choice for RV use in stock form. This is also the difference between this generator, and your older 3500w unit which you said ran everything fine.
The generator can be re-wired fairly easily to put the two windings in parallel so you can get the full 4000 watts in to a single 120v circuit. This is fairly easy to do and is well documented in the Chinese generator thread. I did this to my own Champion 3500 a few years ago, as well as installing a standard NEMA TT-30 jack. Champion now ships their latest model generators with switchable parallel/series windings and the NEMA TT-30 jacks. These are their "RV Ready" models.
Your generator as it sits is not the best choice for RV use. You will always be playing games with extra extension cords and such if you want the full wattage from the unit. You should consider modifying the unit or returning it for something that allows full current to 120V.
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