If you have a 13.5 KBTU HVAC, a 2KW is really iffy. The Yamaha 2400 will run a 13.5 and is about the smallest genset that will.
You would do much better with a 3KW or paralleled 2KWs.
If your trailer has 15 KBTU the 3 KWs are ok to iffy, paralleled 2KWs OK.
If you are not concerned with the noise of a contractor grade genset, you can get by with just about any 4KW+ genset. Very cheap.
Foard County News & Sassy Schoolmarm
with Lady & Chloe, 2013 39 days, 2014 59 days
2017 GD Imagine 2800BH
'07 GMC Sierra 2500HD Diesel 4x4
Why I got into RVing
& More Fun