I would imagine filling oxygen cylinders on the road could be a major pain unless you plan ahead. Make sure you get things taken care of prior to leaving with one of the nation wide suppliers. Lincare is a nation wide DME/home care services, and medical gas fill plant. I would find a national company who could supply oxygen wherever I was.
If you got caught in a lurch, any ER, 24 hour clinic or Firestation could offer help on getting refills.
I'd also suggest you carry a prescription with you to show in case any company wanted to see one.
As far as safe in RV's----- using oxygen would be just like using it in a sticks and bricks home.
I hope your Mom can continue enjoying traveling for a loooooong time!