I learned the Quaker approach to conflict resolution here:

In traditional Quakerism, the process you ask about is modeled on Matthew 18:15-17. If you are having a problem with someone, the first step is to visit with them privately — a setting in which there is no audience, so that neither of you is distracted by a concern about how you look to third parties. There you tell the other person what he is done to distress you, and he tells you what you have done to distress him, and you do your best to work things out.

If that doesn’t work, the second step is to meet again with two or three other parties — Friends you both trust and respect — to help mediate. And if that doesn’t work, you lay your problem before your meeting’s committee of ministers and elders or ministry and counsel. But it is expected of you that you will try step one before proceeding to step two, and step two before proceeding to step three, and step three before telling all the world. Because telling all the world can make things worse —

In each step of this process, a slightly larger number of people are called to really listen and think about what is going on, and make themselves helpful, as a group, to both sides. That’s really valuable.

This Matthew 18-based process worked very well for Friends in most situations for several hundred years. The places where it has notoriously failed have been where belief systems or ideologies were involved — like orthodoxy versus freedom of opinion — because it is very hard to find clear-eyed, impartial third parties in such cases. I hope that is not the case in your own situation!

There’s a very good Pendle Hill pamphlet on all this: Sandra Cronk, Gospel Order. A Quaker Understanding of Faithful Church Community (1991). I imagine it’s out of print, but Pendle Hill has been helpful in providing copies of its out-of-print publications to people who want them.

As a traditional Friend — a member of a Conservative Friends Meeting affiliated with Iowa Yearly Meeting (Conservative) — what meeting for worship is about, for me, is not SILENCE AND PEACE but about waiting on the Lord (a historically important Quaker term): waiting, as a waiter waits on the customers in his charge, or a courtier on a king, for the slightest sign of what her customers, or her king, desire. So it has nothing to do with silence or peace except as a means to better, more faithful listening and taking to heart. And we know, not only from our own hearts but also from scripture, that what the Lord wants, always, includes self-correction, and also reconciliation amongst ourselves. Hearing the Lord more clearly has been, for me, a Herculean task; I came to Friends just full of myself, full to the brim, and it has taken long decades to empty myself to the point where I can at least sometimes hear others without my own self getting in the way. And that is to say nothing of how hard it is for me to hear the God of Jesus, the one who is equally merciful to the just and the unjust, without my own self getting in the way. I am truly a remedial Friend! I have been grateful for every shred of help that other Friends have given me, down through the years.

If I have been helpful at all to you, I am deeply grateful to you for receiving it, and to God for allowing me the opportunity. But I think your own desire to learn, and your own desire for help, are infinitely more precious than my knowledge of how Friends do things. Please keep those desires alive! — so few of us are learners! And God be with you.