Somewhere in the Middle
The truth, it’s always somewhere in the middle of the mess we find.  It’s like the saying, ‘two sides to every story’, except the truth is usually somewhere in the middle of those two sides because our interpretation is always based on our emotions or feeling at any given time.
So what do you do when you have this kind of discontent among your team, or a ‘he said/she said’ kind of situation?  Conflict resolution is a broad term used to explain dispute resolution and encompasses the variety of methods or systems you can engage to resolve conflict.  For example, you can negotiate conflict.  This is where the conflicting parties solve their own problem by talking about their concerns, wants, and needs fact to face. Negotiation allows the disputants ultimate control over the process and the resolution, but can also prove difficult if one or both parties are there to compete and win not resolve or compromise.
Another method is mediation, where you engage a third party who is impartial (important distinction) and they help you identify the issues and work towards a resolution that is mutually acceptable.  With mediation the disputants are not in control of the process itself, but do maintain primary responsibility for the resolution of their conflict.  It’s also called Alternative Dispute Resolution or ADR.
As a leader conflict is likely present each day in some form or another.  How far you allow the conflict to progress is up to you, but if and when you get involved mediation is a good solid approach.  Here is a very basic outline on the process of mediation, which incidentally can be dated back to the 1970’s and credited to the United States.

I.  Assess the Conflict
a.   What is it about?
b.   Who is involved?
c.   At what stage did it escalate?
d.   What is the background each party is bringing to the table?
e.   Is there existing conflict that this is compounding?
f.    What have I not addressed previously?
g.   Where are the rules not clear?
h.   How can I help?
II.  Set up a Mutually Agreeable Meeting Time
a.   Set up a time to meet with the disputants in a neutral, private area.
III. Introduction to Mediation
a.  Explain the process you will follow and include your role as mediator – you will control the process, they speak to you and not each other or whatever suits the situation.
b.  Establish ground rules – for example, no phones, no interrupting, no name calling etc.
c.  Obtain consent from each party to continue. 
IV.  Identify the Issue(s)
a.  Ask each party to explain the situation from their perspective.  Have them speak to you and not the other party.
b. Summarize their perspective, use paraphrasing, check for accuracy after each party provides their perspective.
c.   List the issues and concerns identified.
V.   Problem Solving Discussion
a.  Common Ground – Look for and emphasize commonalities.
b.  Provide Clarity – Attempt to develop mutual empathy and understanding.
c.  Commitment to Resolve – ask the parties to say ‘out loud’ their commitment to resolving the conflict. 
d. Start with the Simple – pick the easiest of the concerns and tackle that one first. 
e. Explore Options – help the parties see possible resolutions.
f. Encourage Team Work – encourage the parties to work together to find solutions.
g. Play the Game – engage parties in the ‘What If’ game where you pose questions about potential solutions or outcomes.
h. Focus the Findings – focus on what is agreeable today that provides peace tomorrow and not on who is right and who is wrong.  Emphasise their interests not their positions. 
VI. Agreement
a. Work out specifically who has agreed to what, when and where or how it will be implemented. 
b.  Ensure that it is fair, realistic, equal and balanced. 

c. Writing things down always adds validity, especially if you have to sign your name in agreement.  Suggest writing it out and having each party sign the agreement.
This is a basic outline that you can morph or change as required to help your team become better at solving conflicts.  If you can show them a method of resolution maybe it’s something they can adopt and use in their own teams or to improve their own skills in conflict resolution.  The fact is, sometimes we just need someone to help us filter our perspective to add clarity and even maturity.  If we are so invested in something it’s easy to become offended or hurt by others who may or may not have the same investment.  As a leader it’s imperative that you not shy away from conflict and that when you face it head on you are systematic, consistent and non-judgmental.  You are the example, be a good one.