We all work with various business partners and stakeholders. Sometimes we run into conflicts with them and progress slows down or becomes even impossible. Make sure you know what the conflict is about. You can present all the facts, but it will not help the situation if the other party disagrees with your methods or goals. Analyze the arguments brought up, discuss the real reason for the conflict, and find your common ground.
You’re under pressure because you definitely started this important project too late. How