Help me pick the perfect camera for my kid

I am in a bind. My DD (14 years old) wants a camera for Christmas.  It has been 5+ years since I have done any serious camera shopping and there are so many choices out there that I am not sure where to start. She is currently using my old Sony compact camera and likes it but it is too slow to capture the images she wants.  Here is a list of her wants in a camera.

1. Compact.  We live on a farm and she will be carrying this around in her hand and pockets.
2. Durable.  See number 1.
3. Fast Response Time.  She takes many pictures of animals and gets frustrated when it takes a couple of seconds for the camera to capture the image and she totally misses the shot.  She mainly focuses on chickens but also does goats, cows and wildlife that we see in the backyard.
4. Sharp clear photos. Since we have wildlife all around us and some of the animals dont like you to just walk up and take a picture.
5. Videos would be nice.
6. Touch screen would be nice.
7. Good battery life
8. Price range would be $150 but would go to $250

Any advise on which camera to begin my search would be much appreiciated.