I have a similar experience, being an adult rider coming back, and finding my horse is really being a pain in the winter! But it's not a problem being an adult, it's just different. Yes, you do tend to get more fearful and maybe overthink in ways the kids don't, but I think I learn faster now, as I'm more invested in reading and thinking about what I'm doing.
As far as tanya's post, she has some good points, but please don't blame yourself for what happened. It could happen to anyone. There are also good reasons for trotting a spooky horse AS LONG as the horse is listening to you. If you have a horse you know is anxious and wound up, and you make it stand, you could end up with bucks, because that energy is going to come out somehow!
I was recently riding my horse who was acting fresh, and asing for transitions (walk trot walk), because I knew he was looking for a reason to spook. My trainer happened to be near by, and she told me to go ahead and let him trot becuase I was just frustrating him by going slow. So it can go either way.
As far as knowing when to lunge, I have learned the hard way (although I did not fall off I did get bucked and I did get scared), that I need to guage the horse's mind set before I ever get on. The day he was nuts, he was nuts from the minute I put him in the cross ties. I should have lunged him first.
Yesterday, he was sleepy in the cross ties, but when we got to the ring eh would NOT listen to me. He would not stand, and so we did some ground work. Then I went to mount and he would not stand, and he would not back up on cue. So I did lunge him. He cantered and bucked and squealed and acted like a crazy thing. Then I got on and he was still keyed up, but at least we had a reasonable ride.
It was frstrating becuase he's been ridden regularly this week, and I didn't expect him to act like that at all. It happend to be sunny and above 32 for the first time in a few weeks, so I guess that was his excuse.
I think my lesson learned is to note when there's been a significant weather change (warmer, colder, windier, sunnier), and also note how they are listening on the ground. If I have any concerns, then I will do more ground work than usual, or lunge.
Good luck to you, sounds like you and I are pretty similar in what we are doing!