I am not a Virginia lawyer and I am unfamiliar with the laws in your state in this area. You will need to talk to a local attorney to learn about the law and your important legal deadlines. However, I can address your situation from a general standpoint.
From a medical malpractice standpoint, I review your facts and cull away all of the stuff about custody and family law. I am sure it is of critical importance to you but it does not affect whether a physician deviated from the applicable "standard of care." Also, malpractice damages are measured by the amount of physical injury to the victim, the medical expenses incurred, the pain, disfigurement, etc. Per the facts you provide, your child is not physically hurt and your primary complaint relates to custody. Unfortunately, I do not see that you have sufficient damages to support a claim. You might have a legitimate complaint to your state's medical board, however.
Again, to get truly competent advice, please visit with a local Virginia lawyer.
Generally, Medical Malpractice cases require a very lengthy face to face interview with your attorney, and then review of the relevant medical records to even begin to evaluate the existence of medical malpractice. Even if the standard of care has been breached, you and your attorney must evaluate whether the case is worth pursuing at all. I agree with Attorney Stewart's answer in this chain, that if there was no harm to the child, that factor would be instructive on whether to pursue a claim or not. The other thing to remember is, such cases are expensive to pursue. YOU must have medical evidence that the physician breached his/her duty and deviated from the standard of care that is expected of a reasonable and competent physician in your community who is faced with the same set of facts...AND...that you (your child) has sustained harm/damages as a result of that deviation. If you are seriously interested in pursuing the matter, you need a face to face meeting with an attorney in your community who handles these matters and be preapred to answer hard questions for that Attorney, starting with EVIDENCE OF DEVIATION OF STANDARD OF CARE? EVIDENCE OF HARM TO THE CHILD? Etc. Respectfully, and if and only if, your question is really more that you are upset at how the parent with primary physical custody handled this matter, dont use the Medical Malpractice Avenue to attack your child's pediatrician. Such an approach will do you more harm than good, if your battle is really a child-custody / parental rights matter. If that is the real issue, do not be baited into bringing a case that you should not bring...its expensive and makes you look unreasonable. Focus on the best interest of the child, and if there really are more effective treatments for the child's medical condition, then present those options as a reasonable parent focused on the best for their child, not a parent who wants to fight anyone who helps the parent with primary physical custody. (If after examining the medical records and reflecting on the whole matter, you believe there has been actual medical malpractice, contact a Virginia trial lawyer who handles Plaintiff's Medical Malpractice cases.) Best- Charlie