I'm not trying to be mean, but you will not be able to go to any outside rental scooter company and have a sure proof guaranteed rental on getting a scooter that will not fail or even be replaced quickly. Scooters are mechanical; so, they can fail. The expectations have to be realistic. You can help yourself by doing all the right things like giving your scooter a full battery charge each night. Don't drive a scooter in the rain; you need to seek shelter until the rain ends. Ponchos help keep the scooter dry, but going over rain puddles can cause issues down below and the poncho won't help in that instance. I still recommend poncos, but that's not sure proof, either. You need to remember to shut off your scooter during times like a parade, fireworks show, or live entertainment shows and so forth to conserve battery power. Bring your battery charger with you everywhere you go. Remember, it can take a very long time to recharge; you don't want to be waiting around at the parks for this process; so, do a good job of recharging every night. I believe Apple Scooters has access to go inside the parks and they have done so as reported here, but not all rental companies do this if the scooter fails. I don't think any rental company is fond of going into the parks and you will wait and wait and wait. Many expect you to manuallly get the scooter back to the resort or whereever somehow. There is a manual lever that allows you to push the scooter in a bad situation. Please verify this aspect of coming right into the parks with whoever you pick; you don't want to be sorry later on. I believe there are some reports on this disboard where people have found kind Disney cast members that have pushed a non-Disney scooter for the guest, but not back all the way to the resort. As a backup, you can get a Disney scooter rental on the spot if there are any left in the park. I know this can defeat the purpose, but at least your person won't have to walk wherever. The process of getting a rental scooter replaced is not a fun situation. Again, the reports on this board ocassionally have shown us this is not a perfect world. For the reasons above some will rent a Disney scooter and pay the extra dollars. There's more peace of mind renting at the parks if there is failure of a scooter and a Disney cast member will help to get the scooter replaced for you. We had this happened and it took about 35 minutes. Again reports here have stated long waits and in some instances misunderstandings from the rental company and they never showed up; until, numerous calls later. It can be a drag if something goes wrong with the scooter. Most of the time none of this happens, but there's that moment every once in a while where it does happen.
We bring a bicycle light with us that can clamp on the scooter. This way you can get a smaller, portable, travel scooter and still have light at night. You can manage without a light if you are very careful. It is easier and better to have a light. A bicycle light cost us less than $10 and it didn't take up much space in the luggage. Bring extra batteries for the headlight. We never had to change our batteries on the light, but it's better to be safe.
I think to me it sounds like you would benefit going to a local mobility store that sells scooters and doing a test run there of a portable, travel scooter. They will let you do this for free with the hope you will buy one. I never feel funny about doing this; because, I will buy a scooter sooner or later. The salesperson will guide you through the process; so, you shouldn't need a rental company at Disney to show you how. Usually you ride around their parking lot of the business to try one out. One of the most popular smaller scooters for rental in the Disney area is a Pride to Go travel, portable scooter. Make sure you learn how to start the scooter; make sure you understand the battery gage and finally make sure you can take it apart and handle it into a car and so forth. Even the lightest scooters can have a piece that weighs 35 pounds. The base of the unit is a little bulky to handle, as well. Usually, the scooters break down to 4 or 5 pieces. Sometimes, this dictates the size of the scooter you will be using. The bigger the scooter the heavier the components are. From your description I think your mom will be fine with the smaller scooter, but it does have less leg room. That's why taking a test drive at a local dealer will help you. All taxi drivers are not willing to dismantle and load a scooter for you, either. Also, you can try out scooters for free at local grocery stores and such for some practice. These scooters are not the same as a portable, travel scooter, but it gives you a little bit of an idea of what to expect. The grocery store scooters are reported to be harder to handle than a lightweight portable travel scooter. Finally, if you can do it many zoos have smaller rental scooters that will be similar to what you might rent for Disney. A day at the zoo would be a wonderful practice session for Disney. Nothing can really prepare you for doing a scooter on and off a Disney bus; this can be challenging for some. In our case, we had to do this for our mother in law; she could not handle getting the scooter on and off the bus. She was still car driving at the time, but she was not use to a scooter and this was difficult for her. I will admit she was 86 at the time; so, maybe, you will have less issue this way with your mom. Don't expect a bus driver to take over the scooter and do this for you; it's a rarity that this would occur. Infact with my MIL, there were other instances where we drove the scooter for her like parking it for an attraction. Even at inside shows we would park it for her and then she would sit on it for the show.
I'm not trying to scare you, but rather I'm trying to prepare you. The scooter is a wonderful answer to enjoy Disney for those with mobility issues, but it's not a perfect world. I hope the pixie dust goes your way and you don't have any issues.