They can do that now through a court order. But if this law takes effect the way it looks they won't be asking for anyone's permission, they'll just go ahead and do it.
No psychiatists and mental health professionals are going to treat children without parental or legal guardian consent. I do not see mandatory treatment requirement mentioned, and I doubt it will pass any constitutional challenge.
To me, this law is just trying to screen for at risk children and postpartum women. I still don't know how they are going to pay for it though.