Does a son commit a sin if he prevents his father, who cannot control his urine and thus causes the mosque to become ritually impure, from going to the mosque except for only one obligatory prayer?

You are not sinful if you convince your father to pray at home; rather, it is obligatory upon you if you fear him contaminating the mosque. If he insists on going out to the mosque, do not let him enter, and try to convince him to pray outside. If he insists on entering and it is possible, have him wear a protective diaper. If it is not possible, do not let him enter, and explain the religious ruling to him. You must treat him with gentleness and kindness, in obedience to Allah and as a reward for him.