Your essay proposal meets the call of the question. Because your goal in writing these essays is to sell yourself to medical schools, I would make sure to explain your thought process and overall approach to addressing this conflict (e.g., I listened actively and respectfully, tried to think through the issue from both sides, offered constructive solutions that would meet the needs of both sides, communicated my concerns in a calm, simple and straightforwrd manner, tried to de-escalate when things got tense, exhibited a willingness to compromise and work with the other side to reach a mutually beneficial outcome, reflected after the fact on what you could have done better, etc.). In other words, show the reader that you thought about and handled the situation in the way adcoms would like to see a good doctor handle a challenging issue. Good luck!