You said that Han Zong defected to Wei because he was worried about being punished for his crimes, which included him using the excuse of his father's death to sit out from a military campaign. But wasn't everyone supposed to spend 2-3 years mourning when their parents died? Why would he be punished for doing what he was supposed to do?
I think you're slightly confused about the sequence of events.
According to Wushu, Han Zong was already planning to defect but was afraid his supporters wouldn't go with him. So he had people set out to plunder, then started telling his followers that the only way they could all be spared is if they defected to Wei. He later lied and said that there was an order for himself and his chief supporters to be arrested for not halting the pillaging, so his followers suggested fleeing. Using his father's funeral as an excuse to gather up all of his relatives, he assembled his family and then fled north.
SGZ proper says that this happened when Sun Quan campaigned against Shiyang in 226. Han Zong was not required to go to the front lines; instead he was allowed to remain at Wuchang because he was in mourning. Sun Quan heard that his followers were plundering but decided not to investigate the matter. However, Han Zong still used his father's death as an excuse to assemble his family and flee.
Later he was killed in battle at Dongxing (253) and Zhuge Ke brought his head to Sun Quan's tomb.
SGZ 55.3 says:
That year, [Sūn] Quán campaigned against Shíyáng, and as Zōng was in mourning, sent him to defend Wǔchāng, but Zōng was unrestrained and violated law. Though Quán because of his father therefore did not investigate, Zōng inside harbored fear,* took his father’s body, and led his mother and family dependents and personal retainers men and women several thousand people to flee to Wèi. *Wúshū states: Zōng wished to rebel, was afraid his attendants would not follow, and therefore secretly sent people to rob and plunder, acted as if he wished to spare them, caused the others to imitate this, and it became the army’s great worry. Later he therefore falsely said there was an Imperial Order, that because the retainers had been lenient to robbers, said: “Officers and officials down are to be together arrested for sentencing,” and also said he feared the crime would reach him. The attendants therefore said: “We can only flee and that is all.” Therefore they together made plans, used the excuse of burying his father, to completely call all his female relatives, wed all of them to his officers and officials, and all his maidservants and concubines he bestowed to his closest followers, killed an ox to drink wine and make blood oath, and with them together made an oath of alliance.
