First and foremost, a match for you and hubby might not be a match for your 3 yr old.
Having said that, you have lots of work to do. This dog might not have been raised with children and has shown that he is willing to go to 'teeth' to keep her at bay. Often dogs who are not raised with kids think they are little aliens and make the dog very nervous. Children move erratically, fall unpredictably, make loud noises, have lots of energy, and look different from adults. It might well be that your child petted too intensely, or squealed a bit, or moved too quickly or got too close. Your dog did what made him feel safe in the moment. NOT excusing it, just trying to understand it.
Never leave your child alone with this dog - do not even turn your back. Only because 3 yr old kids are impulsive and could make a mistake, or the dog could simply make a mistake without much provocation.
This is an opportunity to teach your child how to behave with a dog, NO kisses, NO grabbing, NO Squealing, NO jumping into the dogs space, NO taking toys/bones from dogs, NO pulling on hair, NO hugging. Only calm energy, and lots of space between them unless you are present to take charge.
Find a great trainer to help you teach your dog boundaries, skills and manners. If your dog feels that you are keeping the child at bay then he won't feel the need to step up. If he can do a long down stay in the family room while you all play in the room then he can be part of the family without being in the center of the commotion - which can help him desensitize to the energy of a child. A well trained 'leave it' can help him to learn to back away before he even thinks about getting nervous.
Most importantly, if you step up and teach this dog how to behave then he will begin to look to you for advise when he is insecure/nervous, and if you are ready with the answer/guidance then things can smooth out quickly. The more a dog understands the more confident and calm he should become.
Love Them & Lead Them,
~Elizabeth & Doug
Dog Training the Way Nature Intended