I'm comfortable with our approach for her age. As I noted earlier in this thread, I have found (especially with younger catchers) that getting their body behind the ball allows them to stick the location of the pitch significantly better. Reaching across the body for a pitch puts the arm in a weak position, and the impact of the ball will carry the mitt away from the strike zone. This has a tendency to loose far too many strikes.
Let's look at the video of your dd. I presume she is doing exatly what she was taught to do. She is attempting to catch the outside of the ball, roll the wrist back into the plate, and stick the pitch. She is trying to get her head and chest behind the ball. There are a couple of problems with this methodology. One, attempting to do this puts your dd's elbow and wrist above the ball, creating a weak arm position....something you claim you do not want. Two, your dd is attempting to catch the ball so far out in front of her (essentially barring her arm) it is causing her to move her left knee and chest in order to get to the ball. I know this is a NECC trait as well (receiving the ball with a straight arm) but it causes unnecessary body movement (the catcher is not quiet) for this particular pitch. And three, her head and chest are still moving after the ball is in her mitt. It's not her fault....she is trying to do what she was taught to do. It's hard to virtually impossible to get the head and chest behind the ball in time on a pitch outside of the catcher's body. IMO if she was about a foot closer to the batter, received the ball so her elbow was slightly below and wrist was at the level of the pitch, mitt closer to the body (elbow not barred), reached across her body to catch the outside of the ball and stick the pitch, it gives the impression that much less work was done to receive that pitch on or near the corner, and therefore it had to be a pretty good pitch. JMO.....