You don't want an unsecured 46 lb potential missile behind you in the SUV. Carry it securely in the trailer.
I purchased the Honda EU2000iC a few months ago. There is a valve on the cap with an open/close vent. I keep the genset under the kitchen table when on the road and have noticed absolutely no fumes, whatsoever. Gas will escape
if the unit is not kept upright (tips over), so make sure it is secure.