Ex-etiquette: Celebrate together?

An individual is facing a dilemma regarding ex-etiquette after their former partner requested celebrating their daughter's birthday together annually. The ex-partner argues that shared celebrations are better for the child. Although the parents avoid fighting in front of the daughter, the individual finds being together uncomfortable and believes the child can sense this tension. The situation centers on balancing the perceived benefits for the daughter against the emotional discomfort of the parents during these events.