Hello VCO, I think in some situations grumbling can be a sign of lack of faith. Other times I believe it is due to impatience and not getting one's own way. We are to be about the Lord's way and not our own way.
If you think about the Lord's commands, things he would have us do, much of these are things that are of peace. Things like loving one another, trusting in the Lord, giving thanks, not holding grudges but forgiving one another etc. I see in such instructions help for peace in one's own heart as well as promoting peace with others.
Excellent post.