Dealing with a narcissist is usually challenging. They may go out of their way to make cooperation difficult. It is highly recommended to limit interaction to a bare minimum and, if possible, take a support person with you to witness the agreed matters. A narcissistic person often uses emotional violence and manipulation for their own benefit.
Joint custody requires cooperation, which can be impossible with a narcissist. Stick to the agreement yourself, and don't be flexible about the agreement, as it might become a never-ending one. It might be good to set up a separate e-mail for communicating about children's issues, which you check, for example, once a week. Communicate this openly and stick to your decision firmly.
That's why taking notes, having a checklist made for yourself, having straightforward practices, and accepting all the support available can help you to hold on to what's true and what's not.
It is good to take your own feelings into account. They give a lot of important information, and even intuition can warn of a narcissist.
Do not show your emotions, empathy or aggression. Keep the conversation short, the sentences simple, and stay to the point.
Stick to your decision.