I'm going to address your points step by step.
I never leave my children unsupervised with my dog.
I probably wasn't as clear as I should have been. Supervision is more than just being present. You need to be able to "read" your dog and issue cues to change his behavior before he gets too close to a child, or engages in any preliminary behaviors that are problematic. Not always easy to do, even for experienced dog people.
I was sitting on the floor with my eldest daughter next to me.
Again, I usually suggest that humans be on the higher "resting spot" and dogs on the floor or a cushion if there are any issues whatsoever.
My newborn was in a bouncy seat and my dog in front of me.
One of our other members pointed out that movement engages behavior in some dogs that you may find undesirable.
My daughter kissed the new born and my dog growled then nipped at her shirt.
Especially if she was leaning over the baby, the dog might perceive this as a threat. Frontal approaches, leaning over the body of another animal, and direct stares, not to mention silence and putting the mouth near the child, are all signals that tell some dogs (especially those with limited social experiences involving such encounters) that the threat is real. Also, this dog has experienced pain (even though it was accidental) from the same child falling on her - dogs can put two and two together in ways that a two year old could, so she may be leery of your daughter hurting the baby in the same way she was hurt.
Like I said before, this has never happened with any other infant or child around.
So what? It has now happened, and while it may never happen again, you need to NOT be in denial or excuse it, but rather manage and train the dog so that the chances of it happening again are minimized.
My dog has always taken to people, especially children. I know how my dog acts with young children and she never been aggressive towards anyone, child or adult. At
the same time I can tell when my dog has enough and I separate her from
the situation.
Dogs, like people, do not always love every single other being they meet, even if they seem to like most people or other dogs. You did not intervene soon enough in this case, or you would not have had the incident. Not saying that you even could do so fast enough, but you can see where I'm going with this - dogs are faster than we are most of the time, so the key for now is to keep the dog at a distance during interactions between your older child and your baby.
Maybe this was a freak thing.
Maybe, but don't you want to use more precaution rather than less to insure that it doesn't happen again. Poor interactions with kids kill a lot of dogs - you may be able, if you are NOT in denial, to save your dog from that fate, and have her continue to be part of your family.
My older child and I
playing on the floor with the dog involves and toys like rope, balls,
etc. Playing rough with my dog would be rolling around and playing with toys, never any hitting or pulling.
You don't have to hit or pull at a dog for the dog to think that you are a playmate and not a superior being deserving of respect. Playing on the floor puts you in the same class as other dogs and puppies, and your dog interprets that as a dog would, not as a human would. Stay upright or on a chair as you play with her, and cut out the rough games. Fetch is safer.
There was the occasional falling on the dog but it was never intentional.
That would happen exactly once in my house, if at all. Dogs don't get "intentional" they just get "what just happened to me".
My
dog has never showed any discomfort and it was always followed up by
licking or nudging of the head to the hand for affection.
Nudging is a "demand" behavior that I always ignore, so that my dogs are not manipulating me in any way. Lip licking is a stress related behavior that says "I'm not a threat" and is *not* a "kiss".
The bite was more of a nip and no blood. I did not yell at the dog or show any aggression to the dog.
That shows that the dog has good bite inhibition which, despite the fact that there was a snap, is in your dog's favor. I am glad that you did not show any aggression to the dog, as that might have made a bad association between your older daughter and punishment. Nice going on that one.
Our dog is never allowed on any piece of furniture so I moved the newborn to the couch to diffuse the situation.
That's good, but I would keep baby and daughter off the floor from now on.
I never had a problem like this and didn’t think I needed to take any preventative measures.
Common misconception. ALL dogs need training, management, preventive strategies, and socialization. Otherwise, they just go about doing "doggy things" unfettered...
I
thank everyone for their advise concerning this matter and I hope that
I receive more “how to” posts to help this situation that has taken
place.
Definitely consider going to a positive training class with your dog so that she learns basic commands and you learn some safety and management techniques. One really good thing to do is teach her to watch you immediately when you say her name. The free site, www.clickerlessons.com has a section on "Attention" that's very good.
Thank you again.
You're welcome - everyone here really has your childrens' and dog's welfare at heart.