Am I justified in preventing my wife from playing with and kissing her five-year-old cousin, knowing that we are only engaged, or is my anger exaggerated?

This anger and jealousy are misplaced. A child at this age does not comprehend matters of desire. Allah has permitted a woman to display her adornment before children who do not discern women's nakedness. Ibn Kathir states that the intended meaning of a child here is one who, due to their young age, does not understand the circumstances of women and their nakedness. However, if the child is an adolescent or close to that, such that they understand these matters, then it is not permissible for him to enter upon women. One must be cautious not to raise this issue with the wife, for jealousy in an inappropriate context is detestable to Allah.