Our last 2 trips were with oxygen, and we hadd no problems.
First consideration is the airlines. Are you flying? If so, notify the airline before you get your ticket and find out what their policy is. Will you have to buy O2 from them, or will they let you use your own portable oxygen concentrator. (POC) Also find out if your POC is allowed on board as a carry on item. Not all are approved. You will need O2 at the airport while you wait, and since you can't carry O2 on board (it's considered hazardous) you will need a POC at the airport and also after landing. The O2 company you use can deliver O2 to the arrival gate or even the departure gate, but there is an extra charge for this. If you can borrow or rent a POC from your home supplier that would be great.
If you are driving, a POC is great because they plug into the cigarrette lighter.
Have your home supplier recomend and set up O2 for your stay. You will likely have to rent an oxygen concentrator for the room if you are on high amounts. If you are only on a few lpm your POC might do the job. Talk to your resperatory therapist about your needs and for help in setting it up.
We used Lincare and they were great. We are on high levels of O2 so we had 6 E cylinders delivered. We were able to strap 2 onto the wheelchair, but mostly we only needed 1 at a time. When 4 cylinders were empty we called Lincare and they replaced them with full ones.
Can your mom go a short time without O2? If so, she may be able to do most rides. However, if she needs it steady, I wouldn't recomend any attractions that could damage a cylinder. I'm sure you are aware of the dangers in exploding cylinders. Gentle rides like Haunted Mansion, or the Speedway are ok, but I wouldn't take O2 on any of the mountains or RRC. Fire is ok as long as you are 10 feet away, and of course you would be. The POC is safe on all rides, of course, since there is no O2 inside. However, a rough or violent ride could damage it and I'm sure you would not like to take that chance. We personally felt that the POC was a PITA because it was heavy, the batteries were really heavy, and I was constantly running to first aid to charge them. We found we used mostly cylinders and saved the POC strictly for travelling days.