a parent may not be deprived of his/her parental rights without Due Process (7th Amendment) and a Show of Unfitness.
Indeed. This does not require a trial, let alone a jury.
All the decisions you cite are about custody, or education, or a parent’s right to commit a child against his will to a mental institution, etc. None of them rule out the state requiring vaccination of children, just as it may do of adults.