I am sorry if this has upset you, and you were of course not to know how this would turn out. Starting a thread like this and then not returning to it was bound to end like this.
Of course you, as a new user of MN, could not know this.
You also included no information about what you have done with the dog to help her get used to having a child in the house. There was no mention of training classes or a behavioural report, which is why we have gone on the info in your opening post.
I stand by my earlier statement, however, that you had a responsibility to both your child and your dog, to ensure that neither had the opportunity to (even inadvertently) hurt each other.
You also have the responsibility towards your child to teach her that some dogs don't like to be patted heavily and that she needs to take care around dogs. She was lucky that your dog just gave her a warning nip and did not cause a more serious injury.
She has bitten two children - the first climbed into her bed and the second mishandled her. She has no way of saying, "here, I am not very happy with the way you are treating me", so this is the result.
Having a dog PTS based on the info that you have given would be really wrong. She is not a savage, uncontrollable beast, but a highly strung and nervous dog who would likely be a great pet for a person or couple without young children.