Yes, you got it right, in Star Plus Mahabharata, it's said by Duryodhana, that since Draupadi is now his daasi ('female servant or slave') she has to accept his orders and he can strip her since he's her swami. Was he right? Or is it adharma?
After losing all his brothers Yudhiṣṭhira bets himself and says, should he lose, he'll do anything the Kauravas ask him to:
Sabhā Parva / Dyūta Parva - Chapter 58
Shakuni said, "O Kounteya! You have lost a great deal of riches. You have lost your brothers, your horses and your elephants. Tell us if there are any riches that you have not yet lost."
Yudhishthira replied, "I myself am left, especially loved by all my brothers. If won over, until the time of destruction, I will do whatever deed I am asked to do."
At these words, Shakuni resorted to deceit and told Yudhishthira, "I have won."
And later when they were asked by Karṇa to strip, the Pāṇḍavas do not hesitate:
Sabhā Parva / Dyūta Parva - Chapter 61
When the noise died down, Radheya, who was almost senseless with anger, gripped his lustrous arms and uttered these words...
It has been ordained by the gods that a woman should only have one husband. However, she submits to many and it is therefore certain that she is a courtesan. It is my view that there is nothing surprising in her being brought into the sabha in a single garment, or even if she is naked. In accordance with dharma, Soubala has won all the riches the Pandavas possessed, including her and themselves. O Duhshasana! This Vikarna is only a child, though he speaks words of wisdom. Strip away the garments from the Pandavas and Droupadi.
On hearing these words, the Pandavas took off their upper garments and sat down in the sabha.
So, why did Draupadī disobey the order? What are the rights of a wife and that of a dāsī (female slave)? Aren't wives the property of their husbands? If husband is a slave, doesn't wife automatically become a slave? Bhīṣma seems to agree:
Sabhā Parva / Dyūta Parva - Chapter 60
Bhishma said, "O fortunate one! Since the ways of dharma are subtle, I cannot properly resolve the question you have posed. One without property cannot stake the property of others. But women are always the property of their husbands. Yudhishthira will abandon the entire earth with its riches before he gives up truth. The Pandava has himself said he has been won. Therefore, I cannot resolve this issue. Shakuni has no equal in dice. Kunti's son has voluntarily played with him. The great-souled one does not think he has resorted to deceit. Therefore, I cannot answer the question."
If Draupadī is the property of Yudhiṣṭhira and his brothers, Yudhiṣṭhira staking her after losing himself is an illegal bet and shouldn't have been allowed in the first place. So the question whether Yudhiṣṭhira bet Draupadī before or after he lost himself is moot.
On the question of dharma-adharma in Draupadī's disrobing, against her will, it all comes down to this:
What are the rights of a slave?
Going by Yudhiṣṭhira's words, a slave has absolutely no rights:
If won over, until the time of destruction, I will do whatever deed I am asked to do.
If on the other hand, you agree with these conclusions from G. H. Bhatt's paper, The Draupadīvastraharaṇa Episode: An Interpolation in the Mahābhārata, your whole question is based on an event that did not take place:
There is another evidence in the Udyoga Parvan of the Mbh. (Critical ed.) showing that the Draupadīvastraharaṇa (Dv) episode is a late interpolation. At the instance of Dhṛtarāṣṭra, Sañjaya approaches the Pāṇḍavas and dissuades them from fighting, on philosophical grounds. Kṛṣṇa is annoyed at the sermon of Sañjaya and draws his attention to the atrocities committed by the Kauravas. There is a bare reference to Duḥśāsana bringing Draupadī to the hall but there is no mention of Dv. and catching hold of her hair in Kṛṣṇa's retort to Sañjaya. Later on, Yudhiṣṭhira, also, rebukes Sañjaya and enumerates all heinous offences perpetrated by the Kauravas. Here also, as before, there is no reference to Dv., but there is an allusion to Duḥśāsana's seizing Draupadī's hair only. These are the two occasions where Kṛṣṇa and Yudhiṣṭhira are expected to make a reference to the Dv., if it were a fact at all. The omission of the Dv. event is most significant, and is quite sufficient to prove that the Dv. episode was not part of the original Mbh.
Further, the Karṇa Parvan of the Mbh. (Citraśālā Press ed.) furnishes us with additional evidence. During fighting, the wheel of Karṇa's chariot sinks in the mud, and Karṇa requests Arjuna not to commence fight, on the ground of military code (Ch. 90). At that time Kṛṣṇa criticises Karṇa (Ch. 91) for his hypocrisy, and reminding him of his immoral conduct in the past refers to Duḥśāsana's bringing Draupadī to the assembly-hall, but does not mention the removal of Draupadī's garment, and even the seizure of her hair. Had the Dv. been a fact, a reference to it on such an occasion was necessary, nay, inevitable. Kṛṣṇa's silence on this point is, by itself, an adequate piece of evidence in support of the interpolated nature of the Dv. episode.
The same Parvan, again, furnishes another evidence also. In the Ch. 83, there is a dialogue between Bhīma and Duḥśāsana, before Bhīma fulfills his vow of drinking the blood of Duḥśāsana. In two places, Bhīma refers to Duḥśāsana dragging the hair of Draupadī, but is wonderfully silent on the removal of her garment. Duḥśāsana in reply to Bhīma refers in a boasting manner to his act of dragging Draupadī's hair, but not to that of stripping her of her clothes. If Draupadī's garment was actually removed by Duḥśāsana, it is most unnatural for both Bhīma and Duḥśāsana not to refer to it in the circumstances. The silence on the part of excited Bhīma and arrogant Duḥśāsana, regarding the Dv. episode, naturally leads one to believe that there was nothing of the type in the original Mbh. The episode of Bhīma drinking the blood of Duḥśāsana is, as shown before, a later development; and even this later interpolation does not refer to the Dv.—a feature which naturally raises suspicion about the authenticity of the Dv. episode.
- Besides the internal evidence, there is also some external evidence in support of our theory. The Bhāgavata Purāṇa (Bh) is clearly a work glorifying Kṛṣṇa as the highest divinity, the lord of Vraja and dear to Gopīs. There are in the Bh. altogether four references to the actions of Duḥśāsana which mention only the seizure of Draupadī's hair and are wonderfully silent on the Dv. It has been shown that the Dv. episode was developed with Draupadī's fervent appeal to Kṛṣṇa, the lord of Vraja and dear to Gopīs, with the purpose of magnifying the personality of Kṛṣṇa. One would naturally expect the Bh., a work purely Kṛṣṇaite in nature, to refer to the Dv. episode with an appeal to Kṛṣṇa. But the omission from the Bh. is most significant, and shows that the Dv. episode did not appear in the original Mbh.
The last point for consideration is the society in the times of the Pāṇḍavas and the Kauravas. The only evidence that is available is literary, and that too is scanty. In the Rāmāyaṇa, Rāvaṇa kidnapped Sītā but did not make any attempt to outrage her modesty during her stay in Laṅkā and this shows some culture even on the part of Rāvaṇa, the villain of the sister epic. The literature ranging from the Brāhmans to the Śūdras does not show the moral deterioration which could have made the conduct such as that of Duḥśāsana quite normal. It appears that the society of the Pāṇḍava-Kaurava period was not so depraved as to make Duḥśāsana's action possible. At any rate the moral standard of the Kṣatriyas at the time of the Bhārata battle was far from being low. And this would not leave any scope for the most abominable action of removing the garment of Draupadī by Duḥśāsana in the original epic, which was in all probability a work of pure history.
The examination of the whole evidence available in connection with the Dv. episode, thus, leads us to the irresistible conclusion that the Dv. episode did not form part of the original epic and that it was introduced later on by the redactors of the epic, with motives too well-known. A careful study of the critical edition of the Mbh. and the most valuable foot-notes and the appendices therein, make it possible to find out the several stages in the development of the Dv. episode.
On command of Ambika/Ambalika their daasi visited Vyasa and Vidura born.
Dhritrastra had a son named Yuyutsu from a daasi during Gandhari's pregnancy.
But, such things were not agreed by all daasis. For example, Keechaka asked Shairandhri for the same which she refused. When he forced to do so Shairandhri's husband Vallabh killed him.
In specific case of Draupadi and Duryodhana, it has to be understood that she never became daasi at all, so no such question arises.
In views of Vidura:
Ye Kauravas, take to your heart this high precept that I declare. If virtue is persecuted, the whole assembly becometh polluted. If Yudhishthira had staked her before he was himself won, he would certainly have been regarded as her master. If, however a person staketh anything at a time when he himself is incapable of holding any wealth, to win it is very like obtaining wealth in a dream. ~Sabha Parva: SECTION LXX
It was not Duryodhana, who said this.
It was Karna, who said as follows, to Vikarna, who objected to Draupadi being ill-treated:
O son of the Kuru race, the gods have ordained only one husband for one woman. This Draupadi, however, hath many husbands. Therefore, certain it is that she is an unchaste woman. To bring her, therefore, into this assembly attired though she be in one piece of cloth--even to uncover her is not at all an act that may cause surprise.
Whatever wealth the Pandavas had--she herself and these Pandavas themselves,--have all been justly won by the son of Suvala. O Dussasana, this Vikarna speaking words of (apparent) wisdom is but a boy. Take off the robes of the Pandavaas also the attire of Draupadi.
Coming to the aspect of Dharma, it is very subtle. What Duryodhana and Karna thought to be Dharma, was not accepted by Pandavas and Draupadi. That was why great war occurred.