Is it permissible to reconcile between the children of a Christian colleague?

It is permissible to strive for reconciliation between disputing parties, even if they are not Muslims, for reconciliation is permissible between Muslims and non-Muslims. The evidence for its permissibility between non-Muslims is what Al-San'ani said: "And it is also permissible between non-Muslims, i.e., disbelievers. The rulings of reconciliation apply to them. Muslims were specifically mentioned because they are the considered audience for the address, who submit to the rulings of the Sunnah and the Book."

And the Sharia has permitted kindness to disbelievers as long as they are peaceful, as Allah Almighty said: "Allah does not forbid you from those who do not fight you because of religion and do not expel you from your homes - from being righteous toward them and acting justly toward them. Indeed, Allah loves those who act justly." (Qur’an 60:8) And the verse that encourages reconciliation is general: "No good is there in much of their private conversation, except for whoever enjoins charity or what is right or conciliation between people. And whoever does that desiring the approval of Allah - We will give him a great reward." (Qur’an 4:114) The word "people" in the verse includes Muslims and non-Muslims, as clarified by Ibn Uthaymin.

It is authentically reported in Sahih Muslim that the Prophet (peace be upon him) said: "He is not a liar who reconciles between people, saying good things and conveying good things."