OK - take a deep breath, because the following is a bit long, but maybe go through this info with your Mom, and reassure her
First of all - please let Mom know right off the bat that the controls on most of the rental ECVs are pretty straightforward, and pretty simple. There is a "speed" knob (typically has a picture of a turtle on one side, and a picture of a rabbit on the other side... Hmmm...

) Around these parts, we recommend beginners start on "turtle" and go slow - especially until they feel more confident! Then there is the "throttle" itself - typically either you "squeeze" a handle back towards the tiller, or there is a thumb operated control that you push with your thumb to go. That's about it... no brakes, so you have to learn to watch other bi-pedals (people who are walking) very carefully in case they step out in front of you! (and they will) When you want to stop, you let go of the "gas" and the ECV will stop. And let Mom know that you (and the rest of your travel party) can "flank" her, and form a bubble around her, so that she doesn't have to worry as much about people walking right into her/in front of her.
Once the scooter has been dropped off, the Resort is a *great* place to practice! Here she can practice turning (especially get used to how tightly he can turn) backing up, maneuvering through food service and shops, curb cuts, and - of course - getting on and off the bus! Another great place for daytime practice (if you have some free time in your plans) is Disney Springs; during the day it is often not very busy, and those buses (again during the day) tend to not be as crowded, so it's a good first experience. She can just let the bus drivers know that she is a scooter newbie, and they will help her get on the bus and parked. She will be surprised at how quickly she gets the hang of it! And, if Dad turns out to be an expert "bus parker" then he can park his ECV, walk down the ramp, and ride her ECV on and park it too. The bus driver won't care, I promise!
Do remember to plan ahead a bit on how your group wants to handle things if a bus arrives, and there is only space for 1 scooter/mobility device on the bus. Some groups like to break up and go on, sending half the party with 1 scooter, and the rest of the party on the next bus, and they meet at a designated location. Just be prepared with how your group wants to handle that - you can always wait for the next bus (and be sure to build extra time - let's say an additional 20 to 30 minutes) to allow for a wait for another bus.
And everyone here who has mentioned this is serious: Tell Mom that practicing first (by using the scooter carts at
Walmart, Target, Home Depot, Lowes, etc.) will go a LONG way towards getting her ready for WDW! If she can master one of those giant wheezing beasties... she will be just fine at WDW.
Regarding rain: Some vendors will have a clear "shower cap" to put over the controls; others include a poncho. Obviously, we try to keep our scooters (and especially the exposed electronic controls) as dry as possible, but it's Florida, and you will most likely get caught in a shower at some point. Don't panic - use what the vendor supplies, and they can always wear a standard Parks poncho, put the back of the poncho OVER the seat back (so it hangs down behind the scooter) and put the FRONT of the poncho OVER the front of the scooter to cover the controls, and go on!
I can't stress this enough -
charge the batteries overnight, every night for both ECVs. A rental ECV should be able to go all day at WDW if it is properly and fully charged overnight. The exception to this is if a customer needs a larger size (bariatric) unit, and tries to "get by" with an undersized unit, the battery will drain faster because it is under a greater strain than it is designed for. Make sure the ECV you rent is the right size for the rider!

Both ECVs should be able to fit into any Resort room at WDW.
It's important to have the office hours & availability of your mobility vendor at hand. (in this case, Gold) (Prior to owning my own ECV, I would make an address book or contacts entry in my phone for any mobility vendor I would rent from, so that I could access the number easily. In the "Notes" area, I would include information like office hours, and ask them about emergency after hours information.)
Do take the time to ask the vendor what their current after-hours policy is regarding an emergency - like if the unit stops working altogether (but the battery was charged) or if the battery won't hold a charge at all. Most of the time you will know if there is a problem well before they close the office for the day, but rarely, an ECV will fail later in the evening. If it should happen, find a Cast Member, tell them you need assistance (you may have to ask for a Manager to come help) and then leave a message for the vendor, and follow any emergency instructions they have given you.
Some people will confuse the *cosmetic condition* of the scooter with it's ability to perform. Rental scooters do receive a lot of abuse at the hands of either new users, or careless users ("It's not mine, so I don't care!") and often this shows in the cosmetic condition of the scooter - scuffs, scrapes, broken plastic covers, ripped seats, etc. As long as the unit *performs* - meaning it runs all day on a full charge, and gets you around safely - don't worry about how it looks.
Buy a cheap, colorful bandana, or a roll of brightly colored/patterned grosgrain ribbon from either Walmart or Hobby Lobby (they both sell ribbon and bandanas - pick something you like!) and tie it somewhere on the ECV that is visible. It will help distinguish your parents rentals from a sea of identical rental units outside of rides, attractions, dining, etc. The more you decorate your rentals, the easier it will be to spot quickly!
Last, but not least, snap a couple of photos of the ECVs when they are dropped off (both sides of each unit) and keep your paperwork safe somewhere besides the scooters. Just like when you rent a car, you want to be able to prove the condition the units were in when it was delivered to you. Make sure that the batteries are fully charged when they are dropped off (it should be) and that the charger is with each unit.
Let Mom know if she has any specific concerns, we will be glad to help address those!
And go have fun!