Under the legal sense of the word, "abandonment" occurs when a person disclaims any ownership interest in an item that is not a person. "Abandonment" with respect to a minor child by  aparent of a person in charge of the minor happens when there is no adult supervision of the child for a prolonged period of time.I see no "abandonment" issues based upon what you have written. I see issues with your child's pediatrician where you might be better off seeking another doctor for your child.