So things I'm pretty sure about first:
You have the breaker box wired correctly
You should be able to use the 220 outlet just fine
The 50a/50a cord should be fine, I was somehow under the misapprehension that the generator was 30a for some reason..
The floating neutral thing is a mess and I don't have a coherent answer. I'll try to talk to some of the sparkies at work on monday but I'm not overly hopeful on them helping a lot as its somewhat outside their realm of expertise.
I can say definitively that OSHA requires the neutral/ground bond at the generator:
https://www.osha.gov/OshDoc/data_Hurricane_Facts/grounding_port_generator.pdf
My copy of "RV Electrical Systems by Bill and Jan Moeller" (which is otherwise a pretty good book - yes I have a lot of books
) was no help on the generator side but did confirm the breaker box wiring.
This article was somewhat helpful:
http://www.fohonline.com/current-is...30-generators-and-portable-primer-part-2.html - in particular the section on "“Floating Neutral” Generators" - I don't know if the powermate falls under the "some small inverter generators do not hold their neutral at ground potential, but rather have the hot +60V RMS to ground, and the neutral -60V RMS to ground. These generators cannot have a neutral to ground bond, and are only intended to operate cord- and plug-connected equipment." category but would bet not as its more high end.
My gut reaction is that you probably want the neutral-ground bond back at the generator. If it was me, I would call up a service center and describe the use and ask what the proper configuration is and if they can change the generator for the RV/trailer use case:
http://www.powermate.com/servicecenters.php Its only vaguely possible that they'll be helpful but it can't hurt to try. I would leave the breaker box with the bond disconnected though because you don't want that connected if you hook up to grid power (as you will be tying off of an existing box which will already have a ground-neutral connection and loops there are bad no nos). If you do decide to re-add the bond and the powermate people are unhelpful you can make a special cable that does it inside the cable which is probably about as good (I think the rvdoctor guy linked below describes how).
Some other comments/notes since I was reading stuff:
The bigger problem with romex (since I was re-reading some of that advice in the books I only vaguely remembered from the last time I looked at them) in portable installations is that larger copper wires work harden over time when "flexed" (vibration from the road can suffice to cause this eventually) and then break. The RV Electrical book (and "The Bus Converters Bible" that sits next to it... yeah books..) both recommended "boat wire" which is pre-tinned stranded wire. You have to use crimp connectors or solder the ends though so it is more of a pain than solid. If you aren't moving the trailer much its likely not a problem as there are a lot of old RV's with romex in them it looks like... and most of them haven't burnt down yet
If you haven't I'd cross check all the 110v circuits with a circuit tester:
http://www.homedepot.com/p/Klein-Tools-GCFI-Receptacle-Tester-RT200/203195019#.Umy17yQikwk
You don't need the GFCI testing capability, but its within a buck or two of the one that doesn't have it so.. yeah. tools!
The 220 circuits are nominally harder to mess up (or at least you're suppose to be paying closer attention when you install them
).
If you're ending up using a lot of questionable campground power the RV electrical book suggested upgrading your testing setup to something a like this:
http://www.idealindustries.com/prodDetail.do?prodId=61-165
because it also alerts you to over voltage power and some other conditions that can ruin your camping adventure. They have basically a whole chapter on detecting and correcting bad campground power so I'm guessing its a pretty common issue (or at least used to be the book is from 95). The rvdoctor links below show how to do some more complex/complete testing with a simple ampmeter and handheld hot/cold tester.
And it gets worse - some old campgrounds did stuff like this:
http://www.rvdoctor.com/2001/07/friends-of-gary-mike.html
some good advice here:
http://www.noshockzone.org/rv-electrical-safety-part-iv-–-hot-skin/
and more here
http://www.noshockzone.org/category/rv-safety/ (pages 1 and 2)
(note that he recommends the neutral-ground bond be established as well).