Fighting Yorkies?

We have two Yorkies. I know they can be aggressive, but they are really bad. The older one, about 2-1/2 years old, which we have had longer, is the dominant one and is neutered. The younger one, about 19 months old, is shy and submission with people, but not neutered. We have had them both since they were young, about two months old, so the older asserted his dominance early. Lately, the younger has begun fighting. Not playful, but trying to be harmful, even more. Today, I let the older one in from outside and the younger immediatley began to fight. It was so bad, as I picked up the younger to break them up, he had the older gripped so tightly, I think he was biting his leg, he lifted the older one, too. And would not let loose. Finally got them seperated and kenneled. The older wasn't aggresive, he just walked in the door.

I know neutering the younger would help, but would like to avoid it if possible. But if necessary, we will. Any suggestions before we go that way?