I'd suspect the rawhide is what's giving her loose stools.
As for what happened with the Kong, I'm wondering if she just wasn't frustrated, and gave up when the kibble didn't come out like she she was used to? Not every dog is super food motivated, and the less motivated ones are more likely to give up when getting the food is too hard.
Try giving her part of her breakfast, so that she isn't hungry, and then giving her a smaller sized Kong stuffed with something really yummy, like plain yogurt or canned tripe that has been partially frozen, and see if that works better. If that she goes for that, gradually work up to completely frozen Kongs.
As for what happened with the Kong, I'm wondering if she just wasn't frustrated, and gave up when the kibble didn't come out like she she was used to? Not every dog is super food motivated, and the less motivated ones are more likely to give up when getting the food is too hard.
Try giving her part of her breakfast, so that she isn't hungry, and then giving her a smaller sized Kong stuffed with something really yummy, like plain yogurt or canned tripe that has been partially frozen, and see if that works better. If that she goes for that, gradually work up to completely frozen Kongs.