OK, time for an update.
Thanks for your suggestions. Unfortunately none were entirely suitable (e.g. didn't run as stated, didn't overcome copy protection, etc.)
However, the links you gave me had links to other sites, and I eventually managed to find a suitable application. AoA DVD Ripper (
http://www.aoamedia.com/dvd_ripper.htm) turned "Mean Girls" and "Sleepover" into mp4 files in "real time" (a couple of hours each), and look very good on the iPod. The application had a free trial (10 minutes of converted video) and cost me less than £20.
Oh, and my daughter is happy!
A good result all round - reps to all who helped. Thank you!