Well jogging with her making her run is heavy exercise and is hard on their growing joints. I would say what you're doing now isn't heavy exercise. As long as you exercise her good, she won't want to shred everything in sight up.

It's for her own good to crate her when you're gone, I wouldn't feel bad about it and if you give her like a kong filled with peanut butter while you are gone, she will be fine. I would put peanut butter in the kong, freeze it overnight and give it to her before you leave. My dogs LOVE that.

It keeps her safe and your house from getting torn up, too or having her getting into something toxic or eating something that can cause obstruction and a very expensive vet bill.. so I wouldn't worry too much she is safe in her crate.