He's sizing up the household and trying to figure who's who and he's got Cheyenne figured for the bottom of the pack. He definitely has nothing to fear from her.
He's a big dog and gonna try for the top spot.
I spent a bit of time with Maxx at the shelter. I would disagree that he is trying to dominate your daughter. He actually is a fairly submissive dog. The growling is fear and stress related. It was when he was first left at ACS and I'm sure it is now. He doesn't know he has nothing to fear from her. He just knows she's a stranger that he doesn't trust. Your plan of them rewarding him for good behavior is great. I would add tossing a treat when they walk by in addition to that.
I agree with Jamie that tethering him to you until his fear is past is a good idea. Or at least leave a leash on him so you can grab that to stop him. Other than this issue, he has fairly good nerves and I don't think he would start to guard you. It will give you a chance to stop him before he charges at your daughter or your girlfriend to bark and be scary.
Look up NILIF (nothing in life is free). This is ideal for Maxx. Make him work for everything. If he wants out, he has to sit while you walk thru the door (I was starting to teach him that because I hate it when Jax charges through the door before me). If he wants to eat, have him Down and have your son, your daughter and your girlfriend feed him so he knows the food comes from them too. That will help him learn to trust them.
The Two Week shutdown doesn't mean you can't walk him or play with him. Yes, he does have tons of energy. He's a big puppy. I'm sure he's East German working lines and they are slower to mature from what I understand. It just means take things slow and don't expose him to tons of things. You can play with him in the yard, walk him down the street. He's pretty good on the leash unless he hasn't had any exercise then he pulls. When he did pull, we just took a step back until he released pressure on the leash and once he would turn towards us he was rewarded, sometimes with treats other times by being allowed to go forward.
Good luck! And remember you can call ACS anytime if you need any input on his behavior. Give the goof a good petting for me!