What can I do to keep AirPlay from buffering while playing movie from iPad 2?
The iPad 2 is one of the slowest CPU/GPU that can run iOS 7 and your HD content might be causing the iPad itself to not be able to encode the mirror video. The 7.1 update seems to be better optimized for my older iPhones, so you might retest after updating to the latest OS as well.

You could free up some load by being sure Airplay isn't in mirror mode and is just sending the stream to the AirPlay receiver instead of the screen and the receiver simultaneously.

Additionally, you can try playing SD content (or recording content from the camera and then playing that) to see if it's related to the length of the clip or the encoding. It still could be network congestion, but you might be correct in your diagnosis of the network as performing well enough to stream HD (especially if the Apple TV can stream HD itself and also uses WiFi.)