First of all, you were young and scared and I'm guessing you are remembering it with more "terror" than actually occurred. I worked at a horseback riding stable and the horses learn to take "shortcuts" particularly with kids. We had one horse that would cut a corner and take a shortcut through the woods with just about every rider (we finally put in a fence there so he couldn't do it). The rider was never in any true danger... but I imagine it would be scary for a new rider if your horse goes one way and everybody else's goes another.
Secondly, in your first post the horses were 600 lbs and now they're 1200 lbs... I'm guessing it's like a fish story: they grow with the tellin.'
ONE bad experience with a horse isn't enough to give you and your sister "Equinophobia." A true "phobia" is an irrational fear of something and is often not triggered by any particular event. Just because you're scared or nervous about something doesn't mean it's a "phobia."
The first time I ever rode a horse it was on a trail ride and my horse pretty much did whatever he wanted. I thought it was GLORIOUS because I got to trot when we were catching up with the rest of the group. My mom's horse took her between two skinny trees. We later discovered that one of our friends had ridden the same horse and she did the same thing. These horses plod the same trail day after day and they start developing habits.
My second ride was at a teacher's house (she had invited me over to ride). This WASN'T an old broke trail horse. Something spooked her when we were riding in the field and she took off. I ended up flying out of the saddle. Didn't deter my love for horses one bit.
Ask anyone on this forum and they can tell you loads of stories about falling off horses, etc. and most of us just get up, dust ourselves off, and get back on. ONE hiccup where a horse doesn't go where you tell them to isn't going to give you a phobia.