What is the story of Duryodhana and Subhadra's marriage?

Subhadra

Subhadra was daughter of Vasudev (father of Shri Krishna) and she was sibling of Balram and Krishna. She was extremely beautiful, had large eyes and very pleasant to look at, she was also very modest and humble as she presented herself as milkmaid to Draupadi and Kunti when Arjuna asked her so because Draupadi was unhappy that Arjuna brought Subhadra to Indraprastha.

The story of Balram wanting to marry Subhadra to Duryodhana is not in original Mahabharata but it's mentioned in Srimad Bhagavad Mahapurana. When Arjun was in penance exile, he heard that Balram wished to marry off Subhadra to Duryodhana and except Balram, none of the family members wanted it. So, he went to Dwarka and with the permission of Vasudev, Devaki and Shri Krishna, he abducted Subhdra which greatly angered Balram but after being pacified he accepted marriage of Arjuna and Subhadra.

Duryodhana and Subhadra had no interaction in Mahabharata before or after her marriage with Arjuna.

Source- Shrimad Bhagwat Mahapuran

Who was Subhadra in the Mahabharata?

Subhadra was a very beautiful daughter of Vasudev and she was sister of Balram and Krishna. Arjuna during his penance exile saw Subhadra during a gathering of Vrishnis and Andhakas and immediately fell in love with her. With Krishna’s advice, he abducted Subhdra when she was doing prayers. The warriors of Dwaraka got really angry but Krishna with his words convinced the warriors including Balram to accept the marriage and welcome Arjuna. Arjuna and Subhadra were welcomed in Dwarka where they ritually got married. All this happened with blessings of Shri Krishna because Arjuna would never do such a thing to a sister of his best friend who was also equivalent of his Guru without his permission. The feelings of Subhadra is not mentioned in Mahabharata regarding her abduction but she seems to have happily accepted Arjuna as her husband.

Draupadi initially was salty with this relationship, probably she thought Subhadra was her equal and therefore her rival but on Arjuna's orders she introduced herself to Kunti and Draupadi as a milkmaid and her humility won over Draupadi and she accepted Subhadra as her co-wife.

Source- Mahabharata