Ouch. First bite and the dog should have been allowed out only with an adult and with a muzzle. That he has bitten 5 times and someone hasn't sued you, or the local authorities label him a dangerous dog. Homeowner cancellation or massive increase is also a concern.
For now, I agree with Don... end the door rush. Before you open a door, he's either crated, leashed, or locked in another room with the door closed.
Walks only with a muzzle on, with an adult holding the leash.
Ignoring your youngest? Make him the one and only giver of food, treats etc. Make him do tricks for said food. Tell him to sit, wait however long it takes. He keeps ignoring... put the food up; try again next meal time. It won't take long for him to see your child as worthy of obeying. Once that's down good, start letting the older child do part of the feeding. If you let him loose in a yard, the kids control that also.
As to why he's doing it--- no idea without evaluating the dog. Could be fear, could be protection, could be a lot of things. Could be vision or hearing. Could be thyroid causing aggression. Ask your vet to check for these. If his health is fine, then it may be maturity hitting and showing adult characteristics that you need to quickly fade as possible. Sit in the park and let people run by tossing a treat. Let them start further back, move closer.
And see the behaviorist.
Oh, and share pictures. )) As for the other part of him, a DNA test might help.