Ok, my cousin just called me to talk about the dog situation.
She said the following and she knows my dog personally, FYI.
She said he's a good dog and doesn't have any mental issues. That just because of his "breed" doesn't mean he is bad with children, it depends mainly on the dog owner and the "parenting" the dog has. She said that little dogs tend to run out of patience sooner than big dogs because they think they have to defend themselves more against bigger dogs/kids. So a big dog will take a lot more crap from a toddler because he knows a toddler is too small to really take him on. However, she said the growling from frustration can happen with any dog and it does, every dog has a breaking point (just like us).
She said the growling my dog is doing is DEFENSIVE growling, she said it's different than aggressive growling (which leads to attacks). She said aggressive growling is when a dog is challenging someone because he thinks he is a higher rank in the pack, my dog is not doing this behavior. She also said when he bit her it was more than likely from surprise (because he did a fear bite, not an agressive bite) and his reaction to me (to crouch and show teeth) was a result from a flight or fright response- it's because he was afraid from the bite/crying situation and wanted to protect himself from the pack leader (myself). She said this is normal behavior when a dog is very frightened. And it's likely it will never happen again, especially since he's been normal since then.
She said I need to continue to let my dog know that our daughter is a pack leader too. She said letting my daughter throw his ball for fetch and bringing my daughter on walks to show the dog she is a pack leader will help. She said extra walks will help release any extra stress and make the dog feel more part of the pack.
She said to set up an area in the house where my daughter is never allowed to go. And then teach her that that is the dog's spot and she needs to let him have his space. He can go there when he feels overwhelmed or needs his alone time (which she said is normal for dogs- to want alone time).
She says his growling is normal and his growl is him protecting his toy from a child that keeps taking it excessively. He allows her to take the toy many times (which shows he understands she is at a higher rank otherwise he wouldn't tolerate it at all), but growls when it becomes too much and he is frustrated (which she says is normal, but most people don't see this reaction from their dog because they don't push the dog to this point- children usually do).
She actually laughed when I asked her if my dog is likely to attack my daughter. She said she highly doubts it would happen. She said as long as I am watching them constantly (until she is old enough to understand how to treat the dog), teaching my daughter to give the dog space and showing my dog that my daughter is a top dog in the family, he will be just fine. She said she recommends sitting there with my daughter and showing her how to treat the dog 100% of the time when he is in the house, which means until my daughter gets a better idea of how to treat our dog, he will have to be separated from us a little more. She said it's not fair to him for the next few weeks, but says it will help him understand that I am watching her when she is near him and he doesn't have to become anxious around her.
So that's what she says. BTW, she's been a vet assistant for several years and is getting her veterinary degree soon. She's also a part time trainer during the summers so I definitely trust her judgement.
She said she is dropping by next week to watch the kid/dog interact and will give me some mini lessons and some books to help me out.
Looks like we are heading towards the right direction!