I can think of one way that you might have success, but it's pretty hacky and requires an additional iDevice, some method of connecting the three together wirelessly (either adhoc mode, an iPhone with tethering, or any of the other solutions out there that let up to five devices talk to each other), and the iPads must be jailbroken.
- Install Veency from Cydia
- Install VNC client on your iDevice up front
- Make sure all the iDevices are on the same network (i.e., not each on a 3G connection, but either adhoc'd to each other or to another portable router/3G modem)
- Remote into each iPad as desired via your VNC client. It's not pretty, but once you start the movie, you can stop controlling the iPad. You have control over pretty much everything (including the lock screen, IIRC), as well as volume (via the multi-tasking bar) IIRC, and definitely control over the apps running and videos playing.
All that said, I don't know of any way to keep the kids from playing with the iPad and getting places you don't want them to be (say, Settings), but the above is a start.