Definition: one who intervenes between parties at odds for the purpose of reconciling their differences; serving as a go-between and occupying a neutral position; able to see both sides and draw the sides together; bringing accord

Unsolicited advice is the junk mail of life. — Bern Williams (1929-2003) English moral philosopher
• Mediation is one of the most effective tools of non-violence. It can turn parties away from conflict, towards compromise. — Miroslav Lajcak (1963-) Slovak politician & diplomat

Comment: It would be wise not to intervene, in most cases, unless invited. Although you can be an intercessor, in a sense, as one who prays for the parties at odds.
Sometimes your position includes in its definition the role of mediator. As a parent you are a mediator by default.

Advice: Notwithstanding Mr. Williams’ quote, I have offered advice in this book. I hope some of it is of value to you, but if it does not strike a chord, then indeed, modify it to the best the you and the situation require.