I would have the child professionally evaluated and get a written copy of the assessment and recommended treatment. Once the other parent sees it in writing, failing to acknowledge the special needs of the child would equate to abuse or neglect in my opinion.
I would imagine the one week on/one week off doesn't help the child either. S/he needs stability. When my husband and I divorced, we had shared custody. However, I was the custodial parent, so my son lived with me. His dad would have him every other weekend. My son was ADHD when he was young. It was vital he have a stable environment. Fortunately, my ex was supportive of our son's treatment and counseling needs. He often attended them with us when he could.
It's imperative the parents are on the same page. The only one who suffers from this particular battle is the child. The parents need to realize that and resolve their issues.