Dealing with a conflict means realizing that a battle is going on. To win a battle or to solve the conflict, you need power and breakthroughs.
You have the power and potential to solve a conflicting situation and you need to take action to achieve that.
Design a strategy
Take a white page and write down your options. All of them, even the ones which aren't realistic. What options feel the easiest. Which ones will be successful?
Select 2 or 3 of them and design a strategy, a plan to handle the conflict.
Focus on win-win
Focus on win-win when possible.
Do you need extra info, resources, support or skills before you take action? Is there anything you still need to strengthen your confidence? Go and get it.
After that: take action!
Follow up and repeat your message if needed. Following up is often the key to a definite breakthrough.