So after seeing some of the comments, I was expecting to see a flight of the "let me show you what this baby can do" variety. I hate it when people do that with new passengers.
Instead, what I saw was a guy taking a very nervous passenger for a nice VFR flight. Is the AOA giving goofy warnings? Probably. were you heavy on the stick or otherwise wrong in how you were handling the airplane? Didn't seem like it to me.
Early on, it seemed like there was quite a bit of abrupt banking back and forth, then I realized you're doing some sort of editing voodoo with the tail mounted camera so that it's pretty much staying level with the horizon, not banking with the airplane. I believe that makes all that back and forth look worse than what was probably just correcting for normal bumps.
At this point, I have no idea how many introductory flights or new to GA passengers I've had, but its been a lot. Here are a few thoughts about how I would handle a flight like this. Not saying it's the only right way, or even the best way, just some thoughts about what I would do.
Talk about expectations ahead of time and assure them that I'm not going to give them a roller coaster ride.
Try to fly early in the day before it gets bumpy.
Tell them it's cool if they want to take pictures or ask questions.
Tell them it's a really nice flying day so we may see or hear a few other airplanes.
Explain that if there are a few bumps close to the ground it's because the sun is heating up the earth and it's causing the hot air to rise, which causes the bumps. Just like hitting a pot hole on the freeway and not a big deal. "Bumps" is a happy friendly word, "TURBULENCE" is a scary Evening News word.
I wouldn't do my emergency checklists outloud. We know that it's totally normal, but my new passenger doesn't ever this about wrecking their car so the fact that we're specifically thinking about all these crash contingencies before we even get this death trap off the ground is a little freaky if they're nervous already.
My pre takeoff pax brief is something like:
"hey- this is how the seat belt works and, obviously not expecting this to happen, but if we have to get out of this thing in a hurry, here's how you open the canopy/door/whatever.
This thing that I'm pointing at is like a speedometer in a car, and this other thing I'm pointing at now shows us how high we are above sea level. You can see that right now, it's showing us how high this airport is, which is why it doesn't say zero.
We're going to start rolling down the runway and when we get to about 60 mph we're going to raise the nose a little and the airplane will start flying. We'll continue climbing straight ahead until were a nice safe height, probably around 500' more than what it says right now, and then start a gentle turn on course.
There's going to be some beeping and whatnot, and that's different systems telling me different things about the flight, like whether I've turned the autopilot off for example.
Any questions?"
Overall, I'll say good on you for taking your daughter flying, and good on her for being brave enough to give it a go, even though it's probably not in her wheel house.
Edit; I has one additional thought. We all know that landing is harder than taking off, but when a nervous inexperienced passenger hears that with no frame of reference, what they sometimes hear is "landing is hard, if I do it wrong I'm gonna die" when what we really mean is "landing was way harder to learn, if I do it wrong I'm gonna bounce." They have no clue what the bench marks are, so maybe in retrospect it would probably have gone a long way to say something like, "well, a pretty landing is harder to do than a pretty takeoff, why don't you rate me and see how pretty you think this one is?"