The inclusion of Yosef's parents in the second dream proved that it was prophetic in nature, that Yosef beheld this dreams not as a result of his aspirations of authority, but as a form of prophecy.
Towards the beginning of Parashat Vayeshev the Torah tells of Yosef's two dreams foretelling his leadership role over his brothers. In the first dream he beheld his brothers' sheaves of harvested grain bowing before his sheaves, while in the second he saw the sun, the moon and eleven stars prostrating before him.
While we generally tend to speak of the two dreams together and combine them into a single event, a close reading of the text reveals important differences between the dreams and their effects on the brothers. Most obviously, the first dream depicts Yosef's authority over only his brothers, whereas the second dream refers as well to the "sun" and the "moon," an apparent allusion to Yosef's parents. (As Rashi notes, Yosef's mother, Rachel, had already passed away, and the "moon" referred to Bilha, who assumed the role of Yosef's guardian upon his mother's death.) For this reason, it would seem, Yosef reports the first dream only to his brothers (37:5-6), but tells the second dream to his father, as well (37:10). Since the second dream included his parents, Yosef found it necessary to bring the information to his father, and not only to his brothers.
Additionally, the brothers appear to react differently to the two dreams. After the first dream, we are told, the brothers "despised him further on account of his dreams and his words" (37:8). Upon hearing the second dream, by contrast, the brothers simply "felt jealous of him" (37:11).
Rav Yosef Shaul Nathanson, in his Divrei Shaul (Likutim), suggests that the different reactions to the two dreams resulted naturally from the difference in content. The brothers' resentment intensified after their heard the first dream because they naturally suspected that this depiction originated from Yosef's ambitions of authority and leadership. If Yosef dreamt about their grain bowing to his, the brothers presumed, this could only be because these kinds of thoughts occupied his mind during the daytime hours. The second dream, however, included Yaakov and Bilha. The brothers realized that nobody – certainly not Yosef – longs to see his parents bow submissively before him. The inclusion of Yosef's parents in this vision proved that it was prophetic in nature, that Yosef beheld this dreams not as a result of his aspirations of authority, but as a form of prophecy. Therefore, the second dream did not intensify the brothers' hatred towards Yosef. They understood that he does not harbor megalomaniacal ambitions of power and authority over his brothers, and he beheld these dreams as prophecies of the future.
Nevertheless, even though hearing this second dream did not intensify the feelings of hatred, "His brothers felt jealous of him" (37:11). The recognition of Yosef's dreams as a form of prophecy could not cool the flames of jealousy that burned within the brothers. These feelings of envy likely caused them to dismiss even this second dream as but a manifestation of Yosef's childish fantasies of power, and they therefore felt justified in acting to eliminate their brother from the family, given the threat they thought he posed to the family. Their jealousy blinded them to the obvious but disquieting reality that Yosef was destined to greatness, and they instead attributed his visions to his aspirations of authority.