Unfortunately with Pits, animal aggression is in their nature and no amount of training will change that, but it can be controlled through training. (When he's around other dogs, get his attention with a treat and make him sit, focusing on you until the other dog passes, then give him the treat.) However, human aggression is not acceptable in either of his breeds, but I can see how he could confuse a child at his eye level as another dog through the door, but it is still cause for concern and needs to be evaluated by a behaviorist. Running kids are triggering his prey drive, but he needs to learn that putting his mouth on them while they are playing and chasing with him is unacceptable. Tell the kids to instantly stop running when he puts his mouth on them. He'll learn that by putting his mouth on them, the game is over and the chase stops which means the fun stops. The reason he doesn't bite you when you take him running is because he knows you aren't running away from him, you're running with him.

Does he live outside most of the time or is he inside/outside?