Raising dogs is like raising kids, there is no ONE way to do it. It is only a matter of finding what works for you and the dog!
I will agree first to the training...not so much for your dog, but for you and your family. Being that he is 5 months old and showing this dominance over you at such a young age (the pups age) this is going to be a struggle of you and your family showing him you are all his boss. Being passive with a high energy dog will get you nowhere, so be ready to take the command and follow through with obedience classes. You may even need to take the class more than once. In the meantime, do a google search on the show "It's Me or the Dog" (can't think of her name...Victoria or something) and of course google Cesar Milan. See if you can find something to use from their shows/expertise until you can get your pup into a class to start training. Whatever you do, be consistent. Australian Shepherds require more excercise than most dog breeds. They need training. They are just too dang smart to be a porch dog doing nothing. He will slowly become a nervous wreck if left with nothing to stimulate him.
One question I have is you say he doesn't like to be touched. I wonder if he might have a painful skin condition, or something that might be bothering him physically that you can't see? Besides being given a purpose/job, dogs love nothing more than to be petted and loved on...it shouldn't matter if they are sleeping or not. Only a working guard dog should be on his "guard". I know when I am sick or hurting, I don't want anyone to touch me or bother me. This was a flag that went up. Check his toenails...if his dew claws were not removed, see if he split one. The chipped tooth, did it cause abrasions in the mouth that are making him uncomfortable? Is he chewing on his skin or favoring a leg? Be aware of his movements.
A dog that bites you (especially not accidentally) would make me a wreck knowing there are littler kids (in this case your younger siblings and the neighbor's kids) that are in harms way. Him lunging at the 2 year old is obviously unacceptable. Did you try to correct that behavior when it happened? Or know what to do when that happened? Never try to appease a dog that is in a hyper or nervous state by saying "good boy" or "there there, it's okay" and petting him. You are only reenforcing that negative behavior. He is not a human, or a child. He is a dog, first and foremost, and will feel safer and more secure with parameters and rules to follow.
While I applaud you when you say you are in it for the long haul, I truly do not feel you should paint yourself into a corner should this dog not respond positively to training, your command, and continue to perpetuate his already unacceptable behavior. A dog that bites, should not be rehabilitated by a family, with small kids, that are unsure of what they are doing IMO. If you can not provide a firm hand, PLEASE give him to someone who can. I do agree with Beekissed that a dog with aggressive behavior such as this has only 3 options: rehabilitation, finding a new home, or euthenasia being the absolute last resort. Once you have exhausted all methods of rehabilitation and should he continue that behavior, he is a major liability. That is the hard truth.
You need to put pride aside and think what is best for the dog should you not be able to care for him or meet his needs in training. Allow yourself to think about it. It's okay. Some breeds are not meant for all people. Should this dog be miserable to you, he will be miserable to himself, and you both would suffer the next 15 years just because you are in it for the long haul? That's too dramatic, and not fair to either of you (or your family).
I think you are very smart looking for solid advice and help. None of us are there to assess the situation, so you should strongly weigh the advice you get from your future trainer and your current vet, those that are professionals and will get to see and experience your pup firsthand.
We all wish you the best of luck, and hope your story has a happy ending. Please keep us posted.