T.S.
Our older son (2.5) has a bit of a temper (a gift from Mom). But, in reading your post, I was saying, "Wow." to myself. Jacob went through phases of expressing his anger. For ahwile he would hit. Then he would head-butt things. Then he would throw. Now, he growls and tries to hit us. But, as mad as he gets - it was never as bad as you described.
In my opinion, your 15 month old seems to have a some extremes and I would ask her doctor about it. I recently met a friend for dinner and she has had some pretty challenging issues with her middle son. She met with an allergist and changed a LOT of his foods. It really made a difference. She actually had before and after videos to show the doctors. I never would have thought it could make that much of a difference. If I hadn't have seen the video myself, I wouldn't have believed it.
Good luck.