CPAP and BiPAP with humidifier draws 5X the amperage. If it is possible to not use the humidifier it would make all the difference in the world.
You need to tap into a light circuit wire somewhere to power the device. Use a cigarette lighter socket/plug type connection to the machine.
A group 24 RV battery that powers only a BiPAP with humidifier (and nothing else) will need to be charged after around 12 hours of BiPAP operation. When I was in cold country, I insulated the hose to the mask, and placed the machine under the blankets in order to save energy.
In your circumstances I would seriously consider purchasing a 40-amp battery charger. Like at Home Depot or Lowes. You have too much demand to even think about using solar panels, as the roof area on a camper is small and you would need a minimum of TWENTY amps of panel recharge power. And a 2nd battery to boot. The direct TV receiver used to require around 50 watts itself, and how much do tiny flat panels draw these days...50 watts.??
For batteries, I would look at a pair of group 31 AGM batteries like the Sears Platinum. You've got to size the battery bank and choose a class of battery that will allow the generator/charger to stay at a 40 amp charge rate as long as possible.
This isn't going to be an inexpensive proposition. Otherwise something, somewhere has to give.