The reason for the safety ground lead is...
In the old days the power company, due to a shortage of metals, ran only one wire to your house,, I understand there are still places that are wired this way.. The other (Return) wire was the ground,, This is why folks today conf use Neutral with Ground in some cases.
Now, though today they run a "Neutral" wire, no longer relying on earth ground, The neutral is still bonded to earth ground.
Imagine, if you will that you pick up a tool, say a Skill hand held power grinder (Like a Dremel only heavier duty) and there is a HOT to CASE short. (Before anyone critizes this post be aware I did not choose that tool at random, I actually held it in my hand).
YOU are a path to ground, and thus neutral.. SHOCKING isn't it (It was for me, thankfully not a fatal shock, but I took out more than one grinding point when I went to toss the sucker).
Hence the safety ground, that way you trip the breaker or blow a fuse instead of blowing a human.
With the portable generator the neutral is NOT bonded to ground, thus had I been running that Skill grinder off a generator.. I'd have never known about the short. (OR ruined the grinding points).
I would recommend you replace the plugs on those cords when you can (less you use them EXCLUSIVELY for the generator) and get a 3wire to 3 wire adapter (2 for a dollar at the dollar store) for the genny.
NOTE also: there may be a ground fault on the RV,, Some of them there is no way around that (Some converters, for example, do not play nice with GFCI's) or there may be a way to fix it.. IS it worth tracking down? Don't know.
Home is where I park it!