I'd definitely second the mp4 route.

My husband kindly ripped and transcoded (with software freely available on the internet) a slew of Arthur and Dora dvds for my mp4 player (aka the "tiny tv") and it's brilliant. Not only do you not have to carry DVDs but the battery lasts for ages (8 hours for my player), our daughter can hold it to her liking and it's tiny so it's no big deal to bring.

I would recommend a sturdy pair of earphones though. Ear buds fall out so make sure you get onese with an adjustable over-the-head type.

Best of luck,
K