My heart goes out to you. It's no fun dealing with a bully even if they are only 15 months old. Male or female some little ones are harder to train than others. You can talk to them and try to reason with then until you are blue in the face with no results. I have been there and have done that (23 yrs ago)...lol This is where the quote "Actions speak louder than words." comes in to play.
A dog has far more patients with little ones than you can imagine and your right they do have their limits. Since you have a dog, then you probably know that a dog naturally will nip and growl at their pups (or kids) if they're being unruly and biting. There is always a risk, Kids like pups need training :-)
Like a momma dog you may have to train him on a level he can comprehend (beat him at his own game). Biting him in the same place he bites, or pinching when he pinches...just hard enough to make it hurt (usually does not take much). You can tell what is hard enough by his facial expressions. Then you tell him ouch "that hurts" "no biting" "no pinching" etc.
Sometimes they only way they learn is by experiencing those painful feelings personally. Be sure to back up your actions by disciplining him with a time out. He needs to learn its not a game, not fun and not allowed.
Good Luck, getting a handle on it now will save you many years of grief down the road.
(mother of a aggressive female child)
P.S. Chamomile is a calming herb/flower than helps settle kids down.