I sincerely suggest renting offsite (3 wheel
scooter, no availability issues, and you have it for use outside the parks). I've never seen people have problems with the 3 wheel scooters. As Cheshire Figment has noted, they are much easier to maneuver than the 4 wheelers. On the other hand, I have seen people looking stressed with the 4 wheel WDW ones when trying, for example, to back up when parking between seats at rides.
Here is the list of tips I have amassed.
Start your trip at Epcot, not because the ECV is hard to drive, but because Epcot is the roomiest and it will give your mom confidence.
Since your mom has limited mobility, consider parking the ECV at shows and having her sit on a regular seat. It can be tight at some shows to park (ex: Little Mermaid). Again, not that it is hard, but it is good to remember that she does not have to do it if she doesn't want to.
ALWAYS park facing out (so you can drive right out). It's a pain to have to back up to leave when there are tons of people streaming out. Unless a CM tells you not to, take your key with you.
Take a towel for the seat, it's often vinyl.
When you get the ECV, look in the directions to see where the free wheel knob is. This allows the wheels to move manually so you can push the ECV into place for her. It's good to know this as a backup should your mom freak out. Having a tendency to freak out myself

I like to know it's there.
When getting onto a bus, go in turtle speed and back onto the lift. When you are ready to move, cut the wheel all the way clockwise right away!!! This will back you up in the perfect position to pull into the wc area. If you don't do this, you risk trying to have to parallel park w/o tons of room. If you do this, it is easy. Really!
When taking the monorail, ask which way you will be exiting. Sometimes you can drive onto one side and off the other, sometimes you have to back on or off as you will enter/exit the same door. I prefer to back on and drive off, but quite a few people here do it the other way.
If it rains, it is handy to use a poncho and drape it over your mom & the entire seat of the ECV. I don't know about all rental places, but Walker gives you a shower cap for the controls, which you should not get wet.
Remember that
ECVs have magical powers. You get on one, and POOF, you become invisible. Feel free to say "excuse me" or tell people in back of you as you wait in line on a hill that the scooter will roll slightly back when you start it. Keep moving slowly in crowds.
Feel free to park the ECV so you can walk or stand. I like to walk into some of the smaller shops. I felt weird about this the first time I did it, but the ECV is there to aid with mobility, there is no requirement that you stay in it 100% of the time.
Turtle speed is the slow end of the speed dial and rabbit is the fast end. Turtle gives you greater control for steering even though it is the same speed as going very slow in rabbit. This will make sense once you are on the ECV!
ECVs are great!!! The freedom is amazing. Have a great trip!!!

Cupcake