Parshas Vayeshev features the removal and deceptive use of three garments. Firstly the brothers remove Yosef's garment and dip it in blood and send it to their father implying that it is proof of Yosef's death. Then Tamar allows Yehuda to think she is a prostitute and obtains his cloak among other things as collateral under false pretenses and then sends it to him to see if he will acknowledge it or not. Finally Potifar's wife takes Yosef's garment and presents it claiming that it is proof that he attacked her.
Where else prior to this do we see the deceptive use of a garment? With Yaakov himself. When Rivka had Yaakov dress himself in Esav's clothing to obtain his bracha from Yitzchak. Like the brothers and Tamar but unlike Potifar's wife, Yaakov did not explicitly lie but gave answers that allowed Yitzchak to assume that he is Esav. So too the brothers sent a bloodied garment allowing Yaakov to make the inferences and Tamar sent Yehuda's cloak and other collateral asking him whose these are. By contrast Potifar's wife explicitly lied making false claims about Yosef.
Some might have said that Yaakov's birthright was falsely gained through a disguise. And so his children are taken through three 'removals of garments.' Each of them reveals something about them, tests them by forcing them to confront a situation that allows them to transcend or descend.
The first removal of Yosef's garment shattered the family, sending Yosef off to slavery and the brothers into deception and guilt and Yehuda into an exile among pagans and fathering unworthy children. It revealed the underlying problems and dark sides of the family of Yaakov.
The second removal of Yosef's garment revealed that he would suffer degradation, humiliation and imprisonment rather than transgress demonstrating that he would stay loyal to G-d even in slavery. The exposure of Yehuda's garment demonstrated that even in exile he would place the truth above his dignity. Both Yosef and Yehuda in foreign lands demonstrate that they could prevail in the coming slavery and exile in Egypt.
The act of public humiliation for the sake of the truth prepares Yehuda for his ultimate confrontation with Yosef, to acknowledge what was done and be prepared to accept the consequences paving the way for the reunification of the family of Israel. Where the first removal exposes their 'dark sides', the next two removals allow them to shed them and take on the roles that would bring them to genuine leadership and the descent into exile not as a degraded people but as honored nobility.
Finally this dispelled any doubts about the legitimacy of Yaakov's birthright which had been gained by a disguise, by animal hides and stolen garments. By removing the three garments it demonstrated the weaknesses of his children and also their ability to transcend them and it is that rather than perfection that is the requirement for the nation they would become.