In extreme cases definitely doctors. The problem of parents screwing their kids over medically extends far beyond anti-vaxers. They get a lot of time in the spotlight for various reasons but there are more extreme cases that hit the news occasionally when the media isn't too busy flipping out about some tweet from Trump or some celeberty dating some other celeberty. Things like faith healers, Jehovah's witnesses, Christian scientists, etc. You get the idea. You've all heard the stories.
One such case is very personal to me from my childhood. Nothing to do with religion but my mother was a complete nutter and my sister is lucky to be alive today. Constant visits to shady back rooms of a local health food store called Zerbos, occasional road trips to all over the damn country for these weird homeopathy conventions... Yeah. Not going to go into details beyond that but definitely I would say in extreme cases (and not necessarily just life-threatening ones) let the professionals take control.