+1 for Handbrake. Simply choose an iPad-compatible preset and it will rip and convert the DVD. From there, you can import the video file into iTunes and choose to sync the movie just as you would any other onto the iPad. It can be viewed through the standard Videos app on the iPad, again, just like any other purchased iTunes movie.

As for going through security, I have never taken it out of my laptop bag (which has other cords and such in it) and never had a problem on US travel.