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If the dog was in your yard and was in a fenced area, then it is the parents who were negligent in not monitoring their child so as to prevent her from sticking her hand into your yard.
From a purely legal perspective, when the child's hand crossed over the invisible property line, that is a trespass to property and the parents are then liable for trespassing since it was their child.
So I see no liability here on your part and it was completely the negligence of the child's parents in not properly supervising her that was the cause of the injury.