I agree...my girls are much older than 3 now. They did not have to deal with pat downs.
But I would prepare my children if they were going on a trip. We would play "airport", and go through security. I would let them know we would have to wait in lines and it would be boring. I would have special activites for them on the plane and in line. They were always good as gold. (No screaming or kicking of the seats) Because I prepared them. Why was she afraid of the xray machine? Has she never walked through a doorway before?
Granted pat downs on frightened children or any child is ridiculous. But why was she afraid in the first place? Why was Dad videotaping her? If any of my children were that upset the furthest thing from my mind would be "lets videotape it."