Don't be so gosh danged hard on yourself! So you're nervous, so WHAT??? You've had an experience that would scare the pants off of many people, and most of them would never get back on. You did. Big kudos to you for that!
If I saw you out on the trails, being ponied, I'd certainly not think any the less of you. So many circumstances can lead to a lack of confidence on a horse, who am I to judge? And those that DO judge? You don't need 'em anyway! You, your horse, and your safety are the only things that should matter when you ride.
Tell your instructor what you're feeling when you're nervous, and ask her for exercises to help you conquer it. If trail riding with a big group who likes to go faster than you do makes you nervous, ask a few of the other riders in your barn if they'd like to go for a walking trail ride. (I know LOTS of people who do nothing other than walk on the trails) And then, when that's old hat, and you've made some friends, ask one of them to JOG away from you, but only a few strides, and keep repeating that til you're comfortable. Baby steps.
So what if your kids seem to ride better than you do right now? Kids have no fear, and they certainly don't have the history that YOU have. Hopefully, they never will, because you made an intelligent, informed choice in the horse that you bought for them to learn on.
That is something you should be proud of, not trying to compete with.