That wording means absolutely nothing legally, "not for hire" is a term for a commercial vehicle that is a private carrier, meaning you only transport your own goods and are not paid by someone else to transport goods. But still commercial.
If you are truly and legally not commercial you need nothing on the coach for the dot, and seeing something like you describe on the door is basically a red flag for a dot officer that you are trying to skate and really do have something commercial in the trailer like a race team. If you are a non-commercial rv, that is the whole story and the end of the story. You don't need anything special and just ignore the scales.
If you really are commercial, like a race team or vendor, then you need to go the whole way and get your cdl and usdot number to be legal. According to the dot officer that helped with my usdot setup, if you have one thing in the rv that is used for commercial purpose the whole rig is considered commercial and you need your usdot number, logs, scales, etc. That means if you sell sunglasses at the flea market out of bins in your basement, you are commercial. If you have a race team, you are commercial. Period. There is a lot of bad information out there, and a lot of guys skating, and a lot of guys with their heads in the sand saying "but my buddy has a bigger trailer than me, and he doesn't do any of that...".
As Doc says, if you are truly not commercial, but may look like it due to the configuration of your rig, putting "motorhome" or "private coach" or some such may keep them from pulling you over, but if you aren't commercial, all they will do is let you go anyway.
