force someone to marry not just one, but four other people she never wanted to marry
I'm not sure which version of Mahābhārata you are referring to, but in Vyāsa's Mahābhārata, Draupadī was purchased (vīryaśulka) by Arjuna showing his prowess in an archery contest. It wasn't the usual svayaṃvara where the bride chooses the groom.
Here's how the Purāṇic Encyclopedia defines 'vīryaśulka':
Vīryaśulka (वीर्यशुल्क).—In ancient days the Kings wanted to give their daughters in marriage to the most valiant youths. The custom of showing their valour before the people, before getting the damsel became more prevalent, than giving money to get the girl. Thus marrying a girl by showing his valour is called Marriage by giving Vīryaśulka. (Śulka means Nuptial gift). (Agni Purāṇa, Chapter 4).
Draupadī had no say in how the contest was conducted either, everything was planned by her father (Draupada) and brother (Dhṛṣṭadyumna) with the sole aim that only Arjuna would win the contest.
Ādi Parva - Chapter 176
Having been thus addressed, the Pandavas headed for the southern part of Panchala, ruled by King Drupada. On their way, the brave Pandavas met the great-souled, pure-souled, unblemished and illustrious sage Dvaipayana and paid their respects to him, in accordance
with the prescribed rites. He too showed them his respect and after their conversation was over, on his instructions, they proceeded to Drupada's palace. Those maharathas proceeded slowly, stopping when they saw beautiful forests and lakes. At last, Kuru's descendants, devoted to learning, pure, amiable and sweet of speech, arrived in Panchala. After seeing the city and the royal residence, the Pandavas lodged in a potter's house. Adopting the lifestyle of Brahmanas, they begged for their food. No one recognized those warriors when
they stayed there.
Yajnasena [Draupada] always desired to give Krishna [Draupadi] to Kiriti [Arjuna], Pandu's son, but he never revealed this to anyone...Thinking of Kunti's son, the Panchala got a very hard bow constructed, one that no one else would be able to bend. He had an artificial machine set up above and onto this machine he fixed a golden target.
Drupada said,
He who can string this bow and, after stringing, shoot the target above with these arrows, will obtain my daughter.
With these words, King Drupada announced the svayamvara everywhere.
Debroy, Bibek. The Mahabharata: Volume 1 (p. 440)
After she's been won, neither Drupada, Dhṛṣṭadyumna nor Draupadī herself had any say in what Pāṇḍavas and Kuntī planned to do with her. This is what Yudhiṣṭhira says to Drupada's priest who was sent to inquire about their identity:
Ādi Parva - Chapter 185
...
Yudhishthira then spoke to the Brahmana. "The king of Panchala gave his daughter away according to his wishes and according to his own dharma. He set a price and this brave one has won her in accordance with that. Therefore, no questions can be asked about his varna, action, intention, means of living, lineage or gotra. All those questions have been answered by the act of stringing the bow and striking the target. In doing that, this great-souled one has won Krishna in an assembly of kings. Since that is the case, the king of the lunar dynasty has no reason to regret his decision or be unhappy. O Brahmana! King Drupada's eternal desire will certainly come to be true for the king, because I think that this king's daughter was unattainable otherwise. No one weak in strength or of low birth or unskilled in the use of arms could have strung that bow and shot down the target. Today, it is therefore not proper for the king of Panchala to grieve over his daughter. No man on earth can now undo the fact that he succeeded in shooting down the target." While Yudhishthira was uttering these words, another messenger swiftly came from the king of Panchala, to announce that the feast had been prepared.
Debroy, Bibek. The Mahabharata: Volume 1 (p. 458)
Why didn't Arjuna alone marry Draupadī? Why had to Kuntī intervene and suggest that all five brothers marry Draupadī?
As the conversation between the five Pāṇḍavas below shows, they had developed feelings for Draupadī sometime during or after the archery contest so it's possible the backstory that 'Kuntī mistakes Draupadī for alms and then orders them to share' was invented later to justify five men marrying the same woman which was forbidden at the time. You have to remember that, at the time, the Pāṇḍavas were in hiding so Kuntī must have felt Draupadī is the bond that will keep the five brothers together for the moment and also later in their lives if they were to have any chance of defeating Duryodhana.
Ādi Parva - Chapter 182
Pritha's two illustrious sons went to the potter's house and to Pritha. With happiness in their hearts, those chiefs among men presented Yajnaseni and said, "See what alms we have got." She was inside the house and without seeing her sons, replied, "Share it together." Later, Kunti saw the lady and was miserable at what she had said.
She was anxious not to commit adharma and began to think about what might be done. She took the happy Yajnaseni by the hand and went to Yudhishthira and said, "This daughter of Drupada was presented to me as 'alms' your younger brothers had obtained. O king! O son! As I am in the habit of doing, but in ignorance, I said what I thought was proper, 'Share it together.' O bull among the Kurus! Now tell me how those instructions of mine don't become a lie. How can the Panchala king's daughter not be touched by adharma, committing that which hasn't been done before?" Having been thus addressed by his mother, the wise king Yudhishthira, chief among the Kurus, sat for a while and thought.
He consoled Kunti and spoke to Dhananjaya. "O Pandava! You are the one who won Yajnaseni. It is proper that you should make this princess happy. Let the sacred fire be lit and offerings made. You should marry her in accordance with the proper rites." Arjuna said, "O king of men! Since this is not the law that others accept, do not make me tread this path of adharma. You should marry her first, followed by the mighty-armed Bhima of wonderful deeds, then I, then Nakula after me and finally the energetic Sahadeva. O king! Vrikodara, I and the twins think that the lady should be yours. This is the state of affairs. After reflecting on it, please do what is appropriate, in accordance with dharma and fame and the welfare of the king of Panchala. Instruct us. We are all waiting for your command." Then they all looked at the illustrious Krishna who was standing there. They looked at each other and sat down, her image in their hearts. 'When those immensely radiant ones looked at Droupadi, their love for her arose and put their senses into turmoil. Panchali's charming form was created by the creator himself. It beguiled all living beings and was supreme to all others. Kunti's son Yudhishthira knew from their appearance what was going through their minds. O bull among men! He remembered Dvaipayana's words. Fearing that conflict might arise between the brothers, the king said, "This fortunate Droupadi will be a wife to all of us."
Debroy, Bibek. The Mahabharata: Volume 1 (pp. 451-452)
It's clear from the above the conversation too that Draupadī was not consulted. It's possible she was too young to understand what was happening so a decision was made for her first by her father and later by Kuntī and Pāṇḍavas.
