Resolving a conflict between two direct reports can be a delicate process. Here are steps and considerations drawn from the provided excerpts to guide you through the resolution:

1. Understand the Conflict Modes: Recognize that each individual may have a preferred conflict resolution style, as identified by psychologists Kenneth Thomas and Ralph Kilmann. These styles are competing, collaborating, compromising, avoiding, and accommodating. Assess which styles your direct reports are using and consider how alternative styles might be more effective in this situation. Encourage them to be flexible in their approach to conflict resolution.

2. Clarify Roles and Responsibilities: Role confusion can exacerbate conflicts. Ensure that each direct report has clarity on their own roles and responsibilities, as well as those of their colleague. This might involve revisiting job descriptions, discussing decision rights, and using frameworks like Jurgen Appelo’s (TELL, SELL, CONSULT, AGREE, ADVISE, INQUIRE, DELEGATE) to clarify how decisions should be made within their respective roles.

3. Acknowledge and Address Status and Identity: Consider the impact of perceived status and social identity on the conflict. This could stem from formal hierarchies or social identities such as age, gender, ethnicity, etc. Openly acknowledging and discussing these dimensions can be difficult but is necessary to prevent role confusion and misunderstandings.

4. Facilitate a Dialogue: Engage in a dialogue with your direct reports, employing the principle of "disagree and commit." This encourages an understanding that while disagreement is acceptable, commitment to a unified course of action is crucial. This dialogue should be rooted in empathy and understanding, acknowledging each person’s perspective and emotions.

5. Express Vulnerability and Build Trust: As a leader, demonstrate vulnerability to foster empathy. People do not naturally empathize with those in authority, so you must be explicit about your emotions and rationale behind decisions. This helps build trust and can facilitate a more productive conversation.

6. Assess the Degree of Disagreement: Determine how deeply each party disagrees with the other. Are they simply disappointed, or do they feel betrayed? Understanding the depth of the disagreement can help you tailor your approach to resolution and healing.

7. Invest in Relationship Building: Strengthen the working relationships of your direct reports by encouraging them to invest in understanding and working with one another. This may involve team-building exercises or regular check-ins to address and resolve issues before they escalate.

8. Monitor and Provide Feedback: After the resolution process, continue to monitor the situation and provide feedback. Ensure that the agreements made are being followed and that both direct reports feel heard and valued moving forward.

Remember, the goal is to move towards understanding and away from feelings of betrayal. By handling the situation with care and empathy, and by encouraging open communication, you can help your direct reports navigate through their conflict and work towards a collaborative resolution.