dogs, like kids, really don't exercise themselves. they will play a while, then stop to rest.
Also, she likely isn't getting enough mental exercise. Mushing isn't going to work her brain. I would start doing some obedience work with her. Even if you have to do 10-15 mins in the morning before school and then a longer 15-20 mins in the evening. Then, once a week, spend an hour working with her on different things. Of course, you're also going to have to keep her running and tiring out her body as well.
Also, I would start taking her for daily evening walks. Just a short stroll around the neighborhood - see new places and things. Living in a yard is really no life for a dog. It's BORING to be in the same small area all day, every day.
A dog SHOULD act calmer and "older" in her own yard. It should be the place where she goes to just chill out and relax.
Keeping dogs out of the trash is one of the easiest things to do in the house. You simply put the trash in a can that the dogs can't open or put the can someplace where the dogs can't get it. For 99% of dogs, simply putting a can with a swinging lid on top is enough to stop them from raiding the garbage.