AirPlay Quality Issues from iPad

• Restart both devices and try if AirPlay streaming is fluid again.

If that should not work you can try restoring one or both devices as described in this answer by bmike

Since the iPhone 4S reportedly works, I excluded network bandwith as a posible bottleneck.

iPhone 4S has much more processing power than the 1st gen iPad. If this is not something that used to work and broke, I suspect the iPad is not fit for the task. If it used to work, it could be a software/iOS update that caused it to stop working.

If I understood correctly you are streaming twice: from Internet (Padora) or network computer (Movies) to iPad and then from iPad to AppleTV. You could try to stream directly to AppleTV.