Is she playing with the tree? If so it might be that she is looking for something to keep her busy. She probably likes the tree because it plays with her--the branches bounce, sway and swing back at her. She probably likes this interactive type play much better than the toys you've offered her.
Since you can't be out in the yard with her all the time, the key is going to be giving her something to do out there that is more appealing than attacking the little tree. Do you have a large tree in the garden? If so, you could find a bouncy branch on that tree and tie a rope to it. Feed the other end of the rope through a Kong or other durable chewy toy and knot the end. Now she has a great tug toy that, since it's attached to a bouncy branch, will tug back. Make sure the rope is long enough so that she can reach it easily, but not so long that it drags on the ground otherwise she may just plop down and start gnawing at it, or worse, get tangled in it. You may have to block off the little tree for a short while, and even teach her what her new toy is for, but I bet she'll learn real quick and not bother with the little tree anymore.