I want to know the full story behind the kidnapping attempt of Saindhava or Jayadrada on Draupadi Matha and the outcome of it. I heard he tried to bend Dharma shashtras to get his way but I could not find proper references anywhere.
This incident occurred during the Vanavasa of Pandavas when they were residing in Kamyaka forest. Once upon a time all Pandavas went to for hunting and Draupadi was alone (with maid(s)) in the hermitage, Jayadrtha came there. Jaydratha was going for his marriage to the kingdom of Salwa and he saw Draupadi there. By seeing the beauty of Draupadi his mind filled with evil intentions and he kidnapped her. It is mentioned in Mahabharta, Vana Parva: Draupadi-harana Parva, SECTION CCLXII .
And Jayadratha, the king of Sindhu, and the son of Vriddhakshatra, struck with amazement at the sight of that lady of faultless beauty, was seized with an evil intention. And inflamed with desire, he said to the prince named Kotika, 'Whose is this lady of faultless form? Is she of the human kind? I have no need to marry if I can secure this exquisitely beautiful creature. Taking her with me, I shall go back to my abode, Oh sir, and enquire who she is and whence she has come and why also that delicate being hath come into this forest beset with thorns. Will this ornament of womankind, this slender-waisted lady of so much beauty, endued with handsome teeth and large eyes, accept me as her lord? I shall certainly regard myself successful, if I obtain the hand of this excellent lady. Go, Kotika, and enquire who her husband may be.' Thus asked, Kotika, wearing a kundala, jumped out of his chariot and came near her, as a jackal approacheth a tigress, and spake unto her these words.'"
You may read the next chapters for more details.
When Pandavas returned from hunting they saw the maid was weeping, they inquired about the cause and she told them that Jayadratha has kidnapped Draupadi. After that Pandavas chased Jaydratha and his army and defeated them. Jaydratha left Draupadi and fled from the battle field. Bhima and Arjuna chased Jaydratha. Yudhishthira told them not to kill Jayadrtha as he was the husband of Dussala (sister of Kauravas). It is described in Mahabharta, Vana Parva: Draupadi-harana Parva, SECTION CCLXIX .
And Arjuna said, 'I do not find on the field of battle Jayadratha through whose fault alone we have experienced this bitter misfortune! Seek him out first and may success crown thy effort! What is the good of thy slaughtering these troopers? Why art thou bent upon this unprofitable business?'
Vaisampayana continued, "Bhimasena, thus exhorted by Arjuna of great wisdom, turning to Yudhishthira, replied, saying, 'As a great many of the enemy's warriors have been slain and as they are flying in all directions, do thou, O king, now return home, taking with thee Draupadi and the twin brothers and high-souled Dhaumya, and console the princess after getting back to our asylum! That foolish king of Sindhu I shall not let alone as long as he lives, even if he find a shelter in the internal regions or is backed by Indra himself! And Yudhishthira replied, saying, 'O thou of mighty arms remembering (our sister) Dussala and the celebrated Gandhari, thou shouldst not slay the king of Sindhu even though he is so wicked!'
After that, Bhima and Arjuna chased Jaydratha and caught him soon. Jaydratha was beaten by Bhima badly but Arjuna remind him the words of Yudhishthira. So, Bhima spared his life but shaved his head and left five tufts on his head. Also Bhima made Jaydratha a slave. Later he was freed by Yudhishthira on a condition that he will not repeat the same in his life. It is described in Mahabharta, Vana Parva: Draupadi-harana Parva, SECTION CCLXX .
Vaisampayana said, "Jayadratha flying for his life upon beholding those two brothers with upraised arms, was sorely grieved and bolted off with speed and coolness. But the mighty and indignant Bhimasena, descending from his chariot, ran after him thus fleeing, and seized him by the hair of his head. And holding him high up in the air, Bhima thrust him on the ground with violence. And seizing the prince by the head, he knocked him about. And when the wretch recovered consciousness, he groaned aloud and wanted to get up on his legs. But that hero endued with mighty arms kicked him on the head. And Bhima pressed him on the breast with his knees as well as with his fists. And the prince thus belaboured, soon became insensible. Then Falguna dissuaded the wrathful Bhimasena from inflicting further chastisement on the prince, by reminding him of what Yudhishthira had said regarding (their sister) Dussala. But Bhima replied, saying, 'This sinful wretch hath done a cruel injury to Krishna, who never can bear such treatment. He, therefore, deserveth to die at hands! But what can I do? The king is always overflowing with mercy, and thou, too, art constantly putting obstacles in my way from a childish sense of virtue!' Having said these words, Vrikodara, with his crescent-shaped arrow, shaved the hair of the prince's head, heaving five tufts in as many places. Jayadratha uttered not a word at this. Then Vrikodara, addressing the foe said, 'If thou wishest to live, listen to me. O fool! I shall tell thee the means to attain that wish! In public assemblies and in open courts thou must say,--I am the slave of the Pandavas.--on this condition alone, I will pardon thee thy life! This is the customary rule of conquest on the field of battle.' Thus addressed and treated, king Jayadratha said to the mighty and fierce warrior who always looked awful, 'Be it so!' And he was trembling and senseless and begrimed with dust. Then Arjuna and Vrikodara, securing him with chains, thrust him into a chariot. And Bhima, himself mounting that chariot, and accompanied by Arjuna, drove towards the hermitage. And approaching Yudhishthira seated there, he placed Jayadratha in that condition before the king. And the king, smiling, told him to set the Sindhu prince at liberty. Then Bhima said unto the king, 'Do thou tell Draupadi that this wretch hath become the slave of the Pandavas.' Then his eldest brother said unto him affectionately, 'If thou hast any regard for us, do thou set this wretch at liberty!' And Draupadi too, reading the king's mind, said, 'Let him off! He hath become a slave of the king's and thou, too, hast disfigured him by leaving five tufts of hair on his head.'
But the main outcome of this even was the death of Abhimanyu as I have described in this answer.