Hi there and thanks for the post
I think starting work on the alpha stuff is the best place you could have started. Do you think that it is making a difference?
Make sure everyone in the house is doing the same so the dog really gets the point that it is at the bottom of the pack.
As well as working on the alpha training make sure that you are having a good go at the obedience. Daily sessions for 15-20 minutes are really important to getting your dog to listen to you and also follow your commands when you need him too.
Is he fully vaccinated? If he is it may be a good idea to give him some time out in a boarding kennel for a few days. This can often kick start the change that is needed and give you guys a chance to let things sink in and work out how you want to fix the problems
Otherwise i would recommend the 48 hour ignore method or at least 24 hours.
Now whenever he is being aggressive, whether it be a growl, a nip, a lunge or a bark he needs to get a sudden and strong reprimand to let him know that it isn't on. He needs a loud GRRRRRRR or AHHHHHHH as well as a soaking with a water pistol. Then immediately take him out and into isolation/reflection room.
Give him ten minutes to reflect before going and getting him.
He may spend a lot of time in this room at the start but he needs it so don't feel bad.
The other major important thing is exercise. A long and hard 45 min walk a day as well as games in the back yard can take a lot of the energy out of aggressive dogs and help calm things down.
If you are worried about your kids then a muzzle is a must have. This will protect both you, your family as well as other people and dogs.
At the moment work on these general principles. This should help solve most of the problems but i will be here if you need anymore help at all
Good luck
Todd