Does my adopted dog hate us?

This dog is under socialized and insecure. First off, NEVER leave your child unsupervised with the dog. Both provoke each other, and that's what happened. You CANNOT invite anyone over until you are absolutely sure this dog is secure. She needs a real pack, and she needs to know you are at the top and that you provide food and shelter. Don't pamper her, she needs firm training, not punishment, rewards, and security. She needs to see things in black and white. Get her a crate, tell your kid not to play with her when she is in her crate. Train her to see the crate as her haven and safe, quiet place. Never punishment in the crate. Be adamant in housetraining, and provide a steady schedule that your dog can look forward to. No two dogs are the same, you can't expect one training method to work for another, especially a dog like yours that has bounced around between places. You need to be flexible. I would think your dog is very stressed right now, after not so long coming to a new place, and seeing new people.