Using an iPad as a car entertainment system I am thinking about using iPads with headrest mounts to allow my toddlers to watch videos while we drive. I'd really like to be able to control the iPad from the front seat if at all possible, so that we don't have to get into the back seat and do things like slide to unlock, press play/pause, adjust the volume, etc.

Are there any devices that could be used to remotely control the iPad from the front seat in this fashion?
There is nothing that steps into the iPad at a low enough level as to simulate a swipe to unlock. Even the external keyboard connector could be extended, but that won't allow total control of the device even if you could operate things without seeing the display. There is no concept of a mouse or pointing device in the iOS or the iPad hardware.

You might want to consider a generic LCD panel / speaker system and an iPod touch or iPad with a cable that will reach to the front seats. You could queue up the entertainment and use the video out to present it to the passengers in the back until such time as they can learn iOS and be trusted to hold the iPad. It won't take long for that to happen or for them to show you every hidden feature you never knew existed or could be enabled in the iPad.

This use case screams for an AirPlay video receiver but those aren't shipping yet even in the living room.