There's a HUGE leap from the 3KW level to the 4KW in size/weight. If you can modulate your needs and keep the AC compressor from running while you load up with other items (hair dryers or such) you can get away with a 3KW unit that will be truly portable. I have a smaller AC unit and use a Yamaha 2800 inverter unit. It starts the AC just fine as long as I'm not trying to run the microwave and the TV at the same time. It's QUIET and much less expensive than the bigger/heavier/larger models.
The Kipor units are pretty good value, but the cheapo Chinese units won't last if you're planning on using them on a regular basis. They are also considerably louder which may present issues from time to time. The Honda units are great but VERY expensive. I believe the Yamaha units are just as good as the Hondas and cheaper, albeit just a tad louder (and I do mean tad).
Here are just a couple of websites for outfits specializing in generators:
http://www.electricgeneratorsdirect.com
and
http://www.wisesales.com
Consider weight and size of the unit while considering a purchase. If you can't lift it by yourself, can you move it when you need to? Where will you put it? How loud is it and where will run relative to the "quiet" zones of your trailer (the bedroom, etc)?
FWIW, I have some considerable experience with generators from my motorhomes where I had 12.5KW diesel Onan down to my very portable and very usable Yamaha with Honda 6500's and 10KW's in the mix. The Yamaha is portable and can be used to run a full size fridge & freezer. Any knowledgable generator user will tell you just to run the freezer for a couple of hours every 8 hrs. As long as you don't open the door with any regularity, the contents will remain solidly frozen. Ditto, on the fridge. Just run it a couple of hours every 6-8 hours and everything inside will be in good shape.
If you want something to run the AC, two TV's, the microwave, a hairdryer and the coffemaker at the same time, then you are talking something in the 6KW range but that's not the real world if you just plan a wee bit.