Hi GreenBox,
First of all, I want to welcome you to the Dog Forum. This is a terrific site, and it helped me a lot when I first became a dog owner.
There's a lot that jumps out at me from your post. First, your dog is really, very stressed, and I think he needs a lot of time, patience, and space. This article is a helpful one to read about bringing home an older, adopted dog:
Three Ways to Confuse a New Dog
In particular, please heed the second piece of advice about introducing your dog to too much too quickly. Its author, Patricia McConnell has a wonderful resource book for the owners of newly adopted dogs.
Love Has No Age Limit-Welcoming an Adopted Dog into Your Home: Patricia B. McConnell Ph.D., Karen B. London Ph.D.: 9781891767142: Amazon.com: Books
Next, I would highly recommend that you carefully study all of the resources on this thread:
http://www.dogforum.com/general-dog-discussion/safety-children-babies-dogs-115969/
Honestly speaking, I'm afraid that you are setting your new dog up for failure by allowing so much contact with your toddler while he is clearly feeling very uncomfortable in her presence. It sounds like she's too young to know how to properly interact with your dog, and your dog is doing everything he can to express that he's stressed by her interactions with him, short of biting her. Please listen to what he is telling you.
The resources in that thread will help you learn to identify the subtle signs of his discomfort and show the proper way that children should be taught to interact with dogs. It sounds like you're giving her too many opportunities to provoke him. She doesn't have to hit him to make him feel uncomfortable.
This is another thread very much worth reading:
http://www.dogforum.com/training-behavior-stickies/growling-86338/
Lastly, you've written a lot about "dominance" and about "correcting" your dog. I'm guessing that you have done what many new dog owners do: turned on Cesar Milan and tried to replicate his techniques. The problem with that is that CM is just a television personality. His theories and techniques are very outdated and counter-productive. You will find that almost no one on this site is a fan of his.
What's happening in your case is that every time you "correct" your dog, he's getting more and more anxious and stressed. He's not trying to be the "king" of the household. He's not trying to "dominate" your toddler, or you, or your husband. He's just really, really stressed by his new environment.
This forum emphasizes positive reinforcement training, and we would love to help you develop a better relationship with your dog. I hope that you'll be interested in learning different ways to interact with him. In the meantime, I'd strongly recommend separating him from your daughter.
Good luck to you all.