I've always used a separate
battery rather than tying into the house
battery. Many of today's CPAPs are 24v, so you can't run them directly off the house battery anyway.
For many years, I used an inverter battery with a 12v port and a COAP-specific cable. My wife used to use a pocket-size 12v battery with an accessory port and a similar cable for the CPAP she used at the time.
Both of our current CPAPs are 24v, so another solution is needed. A few years ago, I bought a Transcend machine with a rechargeable battery. It's good for about 1.5 nights, so realistically, you need a way to charge it every night.
If we are going to boondocks, she takes her older machine plugs into the inverter battery. Unfortunately, that battery is reaching end-of-life (17 years) so we need to find another solution for her.
None of these solutions have been inexpensive and all require frequent recharging. We have a
solar panel on the trailer, but haven't tested to see if it will recharge one or both batteries in a day. We do think we could do it while driving based on previous tests.
A key on all newer CPAPs, is to turn off the humidifier. None of the solutions I've mentioned include a humidifier.