As far as I can tell, stories of Shakuni being motivated by revenge are just folklore with no basis in Hindu scripture. The Adi Parva of the Mahabharata describes Dhritarashtra's marriage to Gandhari in completely amicable terms, with Shakuni's father Suvala overcoming his reluctance over Dhritashtra's shortcomings after considering the virtuous qualities possessed by Kuru Dynasty men, and Shakuni happily participating:
Soon after Bhishma heard from the Brahmanas that Gandhari, the amiable daughter of Suvala, having worshipped Hara (Siva) had obtained from the deity the boon that she should have a century of sons. Bhishma, the grandfather of the Kurus, having heard this, sent messengers unto the king of Gandhara. King Suvala at first hesitated on account of the blindness of the bridegroom, but taking into consideration the blood of the Kurus, their fame and behaviour, he gave his virtuous daughter unto Dhritarashtra and the chaste Gandhari hearing that Dhritarashtra was blind and that her parents had consented to marry her to him, from love and respect for her future husband, blindfolded her own eyes.
Sakuni, the son of Suvala, bringing unto the Kurus his sister endued with youth and beauty, formally gave her away unto Dhritarashtra. And Gandhari was received with great respect and the nuptials were celebrated with great pomp under Bhishma's directions. And the heroic Sakuni, after having bestowed his sister along with many valuable robes, and having received Bhishma's adorations, returned to his own city. And, O thou of Bharata's race, the beautiful Gandhari gratified all the Kurus by her behaviour and respectful attentions. And Gandhari, ever devoted to her husband, gratified her superiors by her good conduct; and as she was chaste, she never referred even by words to men other than her husband or such superiors.
And the Bhishma Parva of the Mahabharata describes how Arjuna's son Iravan kills most of Shakuni's brothers during the Mahabharata war, refuting the notion that Shakuni's siblings died in a Kuru dungeon:
The sons of Suvala, however, recovering their senses, once more rushed at Iravat, excited with wrath. Iravat, however, proud of his might, and displaying his lightness of hand, proceeded towards all of them, armed with his sword. Moving as he did with great activity, the sons of Suvala, although they moved about on their fleet steeds, could not find an opportunity for striking that hero (on foot). Beholding him then on foot, his foes surrounded him closely and wished to take him captive. Then that crusher of foes, seeing them contiguous to himself, struck off, with his sword, both their right and left arms, and mangled their other limbs. Then those arms of theirs adorned with gold, and their weapons, fell down on the earth, and they themselves, with limbs mangled, fell down on the field, deprived of life. Only Vrishava, O king, with many wounds on his person, escaped (with life) from that dreadful battle destructive of heroes.
By the way, in revenge for Iravan's killing of the brothers of Shakuni, Duryodhana told the Rakshasa (demon) Alambusha to kill Iravan, as I discuss in this question.