It's all about amps and load. I also have a 89 pace 38' duel duo therms. Think of it this way, when running genset in the perfect world brand new out of the box in the company's test center. The techs crank that baby to the max BOOM and that's what they stamp on the generator 6.5 kw @ 4000 was 120 volts and 33.3 amps. You will never ever get that. Your ac draws 30 amps at min cool so when you crank up the ac you also increase your load to your generator. What's in line is your fuse panel which has a 30 20 amp circuit, and the 20 pops.
On shore power you get a regulated power supply just like you home. So you get for the lack of a better word clean steady power. Generator is not clean regulated power. Another way to look at it think of a garden hose smaller hose to much pressure pop evertime. Large 2.5 fire fighting hose nice regulated flow.
If you really want to test this out, try running a ac , coffee pot and blow dryer at the same time off you generator. The do the same thing off shore.
I hope this helps sometimes I give to much information
You could always think of inverters and more batteries, a little spendy but long-term works great and saves fuel on generator .6 gal an hour adds up when boondocking.