You might be better to investigate Fiamma's range of bike-carriers that will have been designed for leisure-vehicles.
Even a single bicycle can exert a significant leverage on a carrier, especially if the carrier is mounted at the rear of a motorhome that may be moving up and down considerably when being driven on bumpy roads.
I would have thought that, even if you mounted the base part of a carrier on a motorhome's tow-ball, you'd still need to drill holes in the vehicle's rear bodywork to secure the top of the carrier's framework. But it's difficult to comment effectively without knowing what motorhome you've purchased.
It's rare, but not unknown, for the rear wall of a motorhome to be so lightly built that the weight of a loaded bike-rack will over-stress the wall. As carrying bikes is high on many motorcaravanners' wish-list, it's a mite odd that a bike-carrier apparently isn't a commonplace option on the motorhome you've just bought. My own motorhome also has a rear fixed bed and, to fit a bike-rack, I'd anticipatre having to remove the bed's headboard (and very likely the structure that supports the bed slat-framework) to permit holes to be drilled through the rear wall. But that's probably par for the course.
You really need to ask your dealer what's the best way forward. If a 'normal' cycle carrier is impracticable to fit (rather than just irritatingly difficult!), then your dealer should (hopefully) have sufficient experience to advise you on what make/model of carrier could be fitted instead. As a motorcaravanning novice, you very definitely should not be putting yourself in a position where you are guessing that a carrier designed for cars will, or will not, be suitable for a motorhome.