Dog self-mutilating while being destructive?

We have a Great Pyrenees/ Australian Shepherd mix around 6mo to a year old, got her from a shelter. We've had her for probably a month or two now and she's always been destructive when our backs are turned (she's young so we just assumed that was normal.) But recently she has begun tearing things up to the point where her mouth bleeds. We kennel her when we leave and we try hard to make sure everything she can chew is out of her range, but we have a second dog we leave out (Because he is a bit older and no longer destructive) and he seems to be knocking things around and into her range. If she is out and we are home she usually just rummages through trash and makes a mess. It's only in her kennel that she becomes frantic. Is there anything we can do to avoid medication? We're home most all day and she gets plenty of attention, exercise, water and is fed twice a day a good grade of dog. There are also several chew toys in her kennel that she just flat out ignores.