I'll chime in a different way. You are going at Christmas. So, enjoy the shows and entertainment more than the rides. Epcot is number one in that way. There's the Candlelight Processional, different singing groups, and storytellers in World Showcase explaining their Christmas traditions. I guarantee your mom would love doing Disney this way. Your nieces and nephews are new to Disney; so, they can be satisfied doing a mixture of rides and shows. You don't have to do just rides.
You have regular shows to enjoy in every park like the Lion King sow in Animal Kingdom and you can see the parades and fireworks. There are character meet and greets that will give everyone wonderful memories.
Since you are staying onsite at a Disney resort I would utilize extra magic hours and do the early morning ones at each park. The crowds are lower at that time. I would get park hopping passes. I would spend the morning in the early morning park, have lunch there and leave. Take a mid day break back at the resort. Then, go to a different park for the rest of the day. Your mom will appreciate the rest and so will you. You can catch up on your smoking at this time, too. Knowing you will have the time for this should relieve a lot of stress and anxiety. The others can take a rest or enjoy the pool for a while.
With regards to rides and your mom it's best for someone to be ahead of her to help her in and out and someone behind her in case she fell back or whatever. Boat style rides will probably be the most difficult like Pirates of the Carribean in Magic Kingdom. There may be a few instances where you can get your mom close to a ride with the
scooter and get her off the scooter and let someone else park the scooter for the ride. That will be less walking for her. Make sure she is holding on to someone while walking. The Great Movie Ride in Disney Studios comes to mind where this would work well.
Wheelchairs are welcomed on some rides where scooters are not allowed. Maybe, there will be transfer wheelchairs you can use temporarily and park the scooter for the ride queues.
Don't forget to utilize fastpass plus. You need to link everyone in your party for this to work with all of you. You get to make advance fastpass reservations 60 days out for three attractions per day. Once you use those three you can try for a fourth, fifth and so forth on the go. I would use the advanced three fastpasses in the morning. While doing your rest at the resort you can try for a fourth fastpass for your return time to the park.
You can try for
DAS and see what happens there. It may help you. Fastpass helps; so, make sure you utilize it.
If you are not early risers then I think your plan of attack will be much more difficult. The best suggestion then is to alternate rides with shows; so, you can relax a little at a show. Again, your mom will appreciate having a rest.