I can certainly understand being nervous about an ECV after such a scary experience!
But... consider this: Between now and when you leave, you have time to visit local stores (think grocery stores, Wal-Mart, Target, Home Depot, Lowes, etc.) and practice with the store carts.
I know - they are horrible, slow, noisy and it's the last thing you want to do. But these are *excellent* practice for using an ECV at WDW - you have to really focus when you drive these, because they are so horribly crappy (and the controls are loose and horrible from overuse) that if you can master one of these giant, wheezing beasties, a rental at WDW will feel like a sleek sexy race car. Promise!
In all seriousness, consider having a rental delivered to your Disney Resort. Practice with it at the Resort - even taking a 15 minute window to learn hands-on how fast it will go, how quickly you can stop, how tight you can turn a circle, how to navigate through shops and food service (you can practice all that at your Resort prior to going to the Parks) and getting used to curb cuts, ramps and using reverse will all make a HUGE difference in your confidence level.
In the Parks (and at Disney Springs) you will find that quite often, pedestrians (especially children) will dart right in front of you; this is normal, and can be mitigated by having your family walking on either side of you. I tend to drive on the right side, and my family is on the left, so I only have to worry if there are shops on the right where people might step out in front of me.
There are so many folks here who have (like I did) resisted using a scooter or ECV in the Parks. I finally had to realize that using an ECV is simply using a tool - like a calculator to do math, glasses to see better, or hearing aids to hear better - to enjoy my time at WDW. It also gave me my personal freedom; I can get up in the morning, and go down to food service to get a cup of coffee while everyone else is waking up and getting ready. I can go off on my own at Disney Springs to go shopping for what I am interested in, while other family members go in another direction, and then I can meet up with them after they have bought all.the.Star.Wars.things. Ever. LOL
What happened to you is most likely because of an inattentive driver, and I am happy to know you weren't hurt! But don't let that bad experience cause you to discard the use of a tool that could make a positive impact on your trip.
Whatever you do, I hope you all have a lovely time!