Do you get annoyed by my sister playing with my cousin's son, and is my keeping him away from her an indication of a lack of mercy in my heart, and am I sinful for that?

Separating young children of both genders at this age is commendable in Islamic law and is required for their upbringing in virtue, to prevent causes of vice, and to block means of temptation, especially in this era where media has opened children's minds to dangerous matters. This should be done kindly and gently, while avoiding ill-suspicion and accusation without clear evidence.