Rough idle with no load ok with load on kohler 20resal

https://www.kohlerpower.com/home/common/pdf/tp6804.pdf

I'm not sure what you mean by "under load", maybe with a/c on, etc. Also is it really an engine misfire or a rough idle. If it really is a misfire, a scantool at your local parts store should be able to read a code for that. Sometimes a rough idle could be due to just a cracked or disconnected vacuum hose or dirty throttle body. You didn't say whether it runs ok at highway speeds. Sometimes a rough idle can be cleared up a lot with throttle body service or injector flush. Sorry, this is the best I can do with information provided.

Contact Nixon Power Services in TN they can supply you with one

No be careful !!! the muffler is designed to give a certain engine back pressure and emissions. Changing this or piping it out can increase back pressure to dangerous levels. If you build an enclosure make sure the air flow in and out is sufficient and the hot air out does not get sucked back in as cooling air (short cycle) engine damage and fire can result !

I believe your A/C idle up valve may have failed. They do this when hot, but test OK when cold. See here p228

http://www.turboninjas.com/camry/eg1.pdf

Disconnect generator remote start wires in the ATS. Put an ohm meter across the remote start terminals in the ATS and kill utility power, you should here a click in the ATS and the ohm meter should indicate close to zero ohms. If it does then your ATS is fine and the problem is gen control board or wiring between the two. If it does not show that value, then the start relay in the ATS is suspect.

Will it start manually? if so remote ATS issue, if not check battery

bmw should NOT SHAKE THE STEERING WHEEL AT ADLE. OK SOUNDS LIKE ITS RUFF UNDER LOAD LIFT THE HOOD AND CHECK FOR A HISSING SOUND IF SO IT IS VACUUM LEAK. MOST COMMON. iF TAHAT ISNT IT LETS MAKE SURE ITS IDLEING AT 800 RPM IF HIGHER PLEASE PUT ON FORM HERE AT FIX YA AND WE CAN WORK THIS OUT CHECK IDLE, CHECK ENGINE LIGHT, AND THEY ARE BAD AT NEEDING MOTOR AND TRANS MOUNTS MY BET WOULD BE ON MOUNTS

Make sure that the idle is set at 40Hz. You do this by placing a frequncy meter on one of the 120Vac outlets. If frequency is low, the engine will run rough at idle. There is a 3/8 nut next to carberator that needs to be turned to the right to increase the idle speed.