I don't think breaking the skin on numerous occassions and biting in the face is "normal" puppy behavior. Without knowing the dog and seeing the interaction with the owner it is next to impossible to judge what the underlying issue is. It may be aggression or dominance, or it may be that he hasn't learned bite inhibition yet. I really think this needs to be dealt with and dealt with fast because there are 2 kids in the house. The thing that causes me concern is that if you yell "no", his reaction is another bite.
I think you mentioned that Georgie had been returned to the rescue at least once before. I am not sure why they would give a dog who is known to have had some issues to a novice dog owner. Can you go back to where you adopted Georgie from and ask for help? Obviously you don't want to return him but it is also obvious that you need help because you have a dog who (in my opinion) should have not been given to someone with no experience. That being said, Georgie may even be a challenge for someone WITH experience. I don't think you did anything wrong but it sounds like this is a dog who needs a little more work. Most rescue places have volunteers or dog trainer/dog behaviorists and they may be able to help you at no cost, or maybe for a minimal charge.
You shouldn't have to pay $ 155 per hour for a dog behaviorist (which by the way I think is outrageously high, even for CA).
I didn't have that problem with either one of my dogs (I had other problems with them though
- I think every puppy presents a different challenge) but I have worked with people whose dogs have been mouthing excessively. Here is what has helped.
Socialize your dog with other puppies in a controlled environment (puppy classes). They will learn bite inhibition fairly quickly, if they bite a playmate too hard, the other puppy will start yelping and stop playing. Mirror this behavior with Georgie, if he bites, yelp loud and turn away from him. If the yelping doesn't work or it just feels too silly to do it, just say 'uh-uh', or 'too bad', or whatever else comes natural to you and stay consistant with that. Continue to play with him but 3 strikes and he is out, meaning if he continues to bite too hard, he goes in a time out. Keep a leash on him and calmly lead him to a designated area. Contrary, if he licks your hand or behaves, praise him and/or give him a treat.
Basically, teach him gentle = play will continue, painful = play stops.
As you move along tighten the rules a little more and expect less and less interaction with your skin. You can also make him sit, put a treat in your hand, closed fist and put it in front of his nose and tell him "gentle". If he snaps at your hand or nibbles too hard, take the hand away and turn away. Try it again after a few seconds, and give him the treat if he waits patiently and there is no biting. Extend the time that he needs to behave with every session. Try and work on this every day for 5 to 15 min.
I am sure you are not doing it anyway but sometimes it is difficult not to, especially when he bites hard but try and not jerk your hands away. Jerky movements often seem like a game to a dog and encourage them to jump forward or grab you. Never hit or slap as a response to a bite. I know it is often a defense reflex but try and prepare yourself and resist the impulse.
I believe he is only 6 months, so I am sure he is still teething. Give him lots of chew toys. Mine get raw buffalo bones or venison bones. It keeps them happy and their teeth clean.
HTH