My mom watched the video. The video says that the dog had been living with relatives of the owners. The dog was meeting the baby for the first time when the attack occurred.
Of course we weren't there and we don't know everything about the situation. But kicking a dog with no history of aggression (according to the video) out of it's home of 8 years because you had a baby just doesn't make sense. If the dog did have a history of aggression or problems around children, calling an animal behaviorist and working with the dog before the baby was born would be the best thing for both the family and the dog. If the dog's aggression issues could not be resolved, then the family could start looking for a new child free home for the dog.
My mom suspects that there was some type of behavioral problem in the dog's past that had not been addressed, which is why the parents kicked the dog out of the house and kept it away from the baby. Unfortunatley this probably only made the dog angry and caused the dog to see the baby as the reason he was kicked out of his home.
The rescue has some really good articles about kids and dogs that they give to all adopters and to people who contact the rescue asking for help with their dog's behavior problems. Please look at these articles and save them, and pass them on to anyone you know who has kids and dogs.
A Community Approach to Dog Bite Prevention by the American Veterinary Association
Children and Dogs:Information for Parents
Why Dogs Bite: A Guideline for Children
Understanding Aggressive Behavior in Dogs
Nothing in Life is Free
If you have or know someone who has a dog that has aggression problems, please get help, or urge them to get help before it's too late. There are animal behavior specialists that are experienced in handling aggression problems, and they are there to help. It could save your dog's life and save some person, or child, a lot of pain.
Last but certainly not least - please don't blame a breed for problems like this. This could have, and has happened, with many different breeds of dogs, including mixes. Please see the Humane Society of the United States' statement on breed specific legislation.