I've been watching this thread and no, pushing exercises will
not help Brody at all. I agree with Jackie, you have to build a trusting relationship with Brody, and from what you've said, you also have to protect him from
everyone around him.
Trust doesn't come from book reading
but reading your dog! One of the first things you learn when becoming a dog trainer, especially a P+ trainer, is to watch the dog, watch the body language and interact with the dog the best way for that dog. One of the big reasons I pulled Ra Kismet out of the original school he was in was
'because the woman said she wasn't interested in the dog' HUH??? You have to be 'interested' in the dog! If it were a child, would a teacher say they weren't interested in the child, but just there to force learning into their heads! No amount of study, and believe me there's heaps of that in the curriculum of a P+ trainer, will ever replace
actually working with a dog and watching that dog's behavior. Trust is built up over time. It's that wonderful relationship which doesn't happen over night, not even with a puppy who allegedly has no issues at all, even they need time to learn they can trust you. It's a big wide world, with loads of 'scary' things. A young child isn't expected to confront a quarter of what young puppies are expected to confront. When my baby Leaf come to me, she was rescued from an 'abusive environment', she was fortunate to be placed in a very loving foster home. Her foster Mom worked hard (along with her husband) to get Leaf to a point where she didn't shy away from people. But even so, when she came for the meet and greet, I wasn't able to get so much as a tiny pat. I allowed Leaf to 'be herself' I didn't attempt to try to pat her or even get her to come to me in anyway whatsoever!!!!!!!!!!! When, two weeks later, she came to live with me I did the same thing, just let her run around the house, checking out everything (and yes a small wee on the floor) and I didn't start 'working with her' for around a week, when I was sure she had started to find trust in me. Since then, with the help of my older dog Zeus (whom she trusted straight away) she has over come her fear of going on walks, other dogs, people, scary 'big boy toys' like the trash truck, heavy rain (though she still isn't keen on getting wet

) and a myriad of other 'scary things'. But I had to 'earn' her trust first! You've read so much, now is the time to really start working on what you've learned and, most importantly, gaining Brody's trust in you. Trust doesn't come from a book, it comes from interacting and understanding your dog, spend less time in the books and more with Brody. Just have fun together,formal training isn't everything, play, talk to him, have FUN!!!!!!!!!!!!
At present the poor boy isn't sure who to trust, he's one confused dog. Go back to total basics with him, very tiny baby steps, and I mean
tiny jumping from one training method to another isn't going to help him at all! Thank goodness you refused the prong collar, that would have made him even worse. Patience, loads of patience, is a big key to training dogs (or any animal) whether they have issues or not. Brody will not become the dog you want in your time, but with patience he will become a well mannered, well behaved boy in his time. And if that's years not months, so be it. He may never be a 'social butterfly' dog, but prefer just his exclusive circle of friends, again so be it. Not all people are extraverts some are introverts, dogs are exactly the same. Some thrive on attention, adore the world and everyone in it and others are more the reclusive types who prefer to be with just their companions.
That Brody has nipped people
without any warning growl isn't a good sign, as it means
he's given warning signals before and they have been ignored!!!!! Dogs do not bite without first giving a warning and if that warning is ignored, then they will escalate their feelings. That he's nipped is level one, there are seven levels of biting from nipping without breaking the skin up to the serious, sutures required bites. He's on level one at this stage, so watch and work with him and don't let him have to step it up a notch. He may not have growled but his body language would have shown that he wasn't happy with the situation. Has he ever growled at anyone before? And, if my memory serves me correctly, the nipping of your daughter's friends was because they reached over a gate, something many dogs, not even well socialized dogs, will not permit as it's an invasion of 'their home/territory'.
The best thing you could learn right now is Dog Body Language, get that firmly into your head, so that you know the moment or even before if you're very quick and perceptive, when Brody is about to over-react.
That he's bitten you by mistake - boy he must have been totally over the threshold - dogs do not bite the ones who work with them, especially if that person has been kind to them, unless they are TOTALLY in the 'red' zone. Ra Kismet, who didn't have a nasty bone in his body bit me on the hand when he zoned out after he was attacked. The reason is that the dog has developed 'tunnel vision' they do not hear, see or think about anything other than what is causing them to over react. They get the proverbial 'red mist' come down and they literally do not even know they've bitten you. So don't be afraid of Brody now because of that incident, it really will not help one bit. Just realize he was totally over the top, re-directed on you but not because he actually meant to hurt you, but because he wasn't really 'with' the world at that point of time. It happens, especially if the dog is really afraid of something.
You've only had Brody seven months, a very, very short time for a dog with 'issues', dogs are living, breathing, thinking creatures and, like humans with issues, are not 'cured' over night, or in just seven months. It can, as with Jackie, take years and years to over come the issues. With Brody, to be very blunt, some of his issues stem directly from his home environment. He's totally confused and who can blame him??? You love him and are doing your best, some of your children love him, whilst he has a man (your husband) who wants his respect but doesn't give a damn about him. Would you give respect to someone who couldn't care less about you especially as that person is in your 'safe place' your home where you expect to be loved and respected? Look at it from Brody's view, put yourself in his paws. Plus a daughter who sends him completely mixed signals.
As Jackie as said, sadly, maybe having a dog isn't right given your husband's attitude (and also your daughters hit and miss attitude). I would suggest thinking very seriously about this factor, as I know from all your posts, you really want what is best for Brody. Maybe a home were he's wanted by everyone may be the only answer. Or just