I have found what works for me in the past is to bring my toddler along and have her wear a pilot hat from the airline she is flying (usually Delta). I then have her run up to the flight attendant where she generally gets lots of ewwws and ahhhs and then I broach the subject about how neat it would be to get her picture in the cockpit.

I'm not afraid of flying though. So, I can't comment on that. I could cite all the statistics of how much safer it is than driving, but I am sure you know those already.

Have you thought about calling United customer service and asking how you might go about it? Alternately, there are some pilots and airline personnel on this forum- perhaps they can chime in.