OP - So sorry that your daughter got banged up! I hope she was able to enjoy the remainder of her vacation without too much discomfort.
It can definitely take a hot minute to get used to Irving a vehicle with no brake, unless you are a seasoned driver of an electric car! A lot of other factors can play a part, though. 3-wheeled
ECVs are very agile in the sharp turns found in most queues, but many new users do need to get used to how sharply they can turn, and how to control their speed while doing so. Travel companions can be a big help by showing patience, as well as preventing other parties from crowding up too close in those situations.
The most important thing
ECV drivers must prepare themselves for is often being under a cloak of invisibility. That is my only explanation why pedestrians will step directly in front of you, or cut you off ruthlessly with their strollers. This will happen A LOT. Expect it. Anticipate it. Pretend you are navigating a kindergarten playground at lunchtime. It bites, but the reality is that these vehicles are motorized and can inflict a lot of damage, even when not at fault.
This may sound very negative and I assure you that it is not meant to discourage anyone who needs to use an ECV. They are wonderful devices which let you and your companions experience the trip far more comfortably. If someone is feeling very insecure about driving an ECV, please do practice before you travel, if possible. Many stores offer them for the mobility-challenged customers. If confidence and competence cannot be established, consider a wheelchair, provided there is someone willing and able to do the pushing.
Let me relate a happy experience from years ago. My 89 yr old mother was briefly introduced to an ECV at our resort and drove it happily for 10 days in WDW. She recognized her weak spots, though. Thick crowds after dark were way out of her comfort zone. DH and I would slip the device in neutral, push and steer it, with her in the seat. Or one of us would drive while Mom walked for a while. She took it over a curb once, but we were right there to make sure she did not panic or tip. She loved the ECV and particularly enjoyed the times when she had some wide open space to feel the “freedom of the road” as she missed driving a car. We have a cherished(???) memory of her zooming along a walkway along the edge of the Epcot parking lot, snug in her rain gear, while I chased her in the downpour as she was going further and further from our parked car. I was soaked, she was apologetic, and we laughed so hard we nearly cried.