Was the questioner right in refusing to help an agitated man who claimed his mother needed his help on his way to the mosque, preferring to pray instead, and what is the correct action in such situations?

Going to prayer in this situation is the correct action if you do not have the money the man needs. In such cases, one prioritizes what one fears will be lost, whether it be a life, the damage of a limb, or money, over prayer, even if the money is little or belongs to a disbeliever. Scholars have stipulated that prayer should be interrupted if one fears the destruction of a protected life or the loss of property.