How should Reformed people deal with Wrong doctrine? Question for Calvinists/Reformed people!

There are some teachers in my Evangelical church who teach Salvation by works to the  children in the church. Their Justification for this is make the children behave well. I have judged this as dishonouring to GOD and his Word - and have confronted them on several occasions on their doctrine. 

Because I have done this several times, fellow church members have accused me of dividing the Church, disturbing the peace and being intolerant. 

I am working with the challenge of both When to speak up and how to speak up. 

When?


When should I correct faulty doctrine?
When should I refrain?
Does the Bible have a 'formula' for correcting doctrine (like Matt
18:15-17)?


How?


If you have ever confronted somebody on their doctrine, could you
please recount how you did it?
The typical Reformed perspective on this is that the teachers of the church should not be teaching doctrine which disagrees with the confessional position of the church (which in continental Reformed churches is typically the Apostles' Creed, Nicene Creed, Athanasian Creed, and the Three Forms of Unity; in Presbyterian churches, it is typically the same creeds and the Westminster Confession of Faith as far as I know).

If an official church teacher is teaching doctrine contrary to the confessions the church upholds, then it is definitely your right (and duty!) bring the matter to the Consistory of your church (e.g. the minister/s and elders). Most Reformed churches have an article in their church order regarding this (in the case of continental Reformed churches, usually based on the old Netherlands Reformed Church Order:


  Article 75
  
  The reconciliation of all such sins as are of their nature of a public
  character, or have become public because the admonition of the Church
  was despised, shall take place, when definite signs of repentance are
  evident, publicly, by the judgment of the Consistory; and in rural
  districts or smaller towns having only one Minister, with the advice
  of two neighbouring Churches, in such a form and manner as shall be
  judged to be conducive to the edification of each Church.
  
  Article 76
  
  Such as obstinately reject the admonition of the Consistory, and
  likewise those who have committed a public or otherwise gross sin,
  shall be suspended from the Lord's Supper. And if he, having been
  suspended after repeated admonitions, shows no signs of repentance,
  the Consistory shall at last proceed to the extreme remedy, namely,
  excommunication, agreeably to the Form adopted for that purpose
  according to the Word of God. But no one shall be excommunicated
  except with previous advice of Classis.


And also later in Article 79, elders or ministers who preach false doctrine or heresy (which in the example you gave, would be the case) should be suspended and/or deposed, as well as disciplined as per the quoted articles.

The reason the complete Matthew 18 process is partially skipped is because publicly teaching confessionally false doctrine is a public sin, and as such should be publicly admonished, skipping private admonition.

If someone is not publicly teaching false doctrine, but does subscribe to it, and it is a confessional doctrine, then you should follow the Matthew 18 process to admonish them and restore them to the faith. This is also described in the linked church order. 

Regarding when to NOT try to correct false doctrine, if the matter is not confessional then you don't typically need to follow the Matthew 18 process. This is because any non-confessional matter is not considered necessary for salvation (and typically there is debate on the matter, among orthodox scholars). For example, falsely taught soteriology is a confessional doctrine and thus MUST be confronted. But having a disagreement with someone about whether or not the burning bush was the first or the second person of the Trinity is non-confessional, and as such not something that should be disciplined by anyone but God.

The Presbyterian position may differ somewhat, and I would be interested in seeing an answer from that perspective.