In the Mahabharata, Yudhishthira justifies his polyandrous relationship with Draupadi with two reasons: it has historic precedent, and because his mother ordered the Pandavas to share Draupadi:
"Yudhishthira then spoke, saying, 'My tongue never uttereth an untruth and my heart never inclineth to what is sinful. When my heart approveth of it, it can never be sinful. I have heard in the Purana that a lady of name Jatila, the foremost of all virtuous women belonging to the race of Gotama had married seven Rishis. So also an ascetic's daughter, born of a tree, had in former times united herself in marriage with ten brothers all bearing the same name of Prachetas and who were all of souls exalted by asceticism. O foremost of all that are acquainted with the rules of morality, it is said that obedience to superior is ever meritorious. Amongst all superiors, it is well-known that the mother is the foremost. Even she hath commanded us to enjoy Draupadi as we do anything obtained as alms. It is for this, O best of Brahmanas, that I regard the (proposed) act as virtuous.'
But polyandry is a non-Vedic practice:
Aitareya Brahmana III. 3. - Therefore, there are several wives for one man, but not several husbands for a woman simultaneously
In the MB section linked above, even king Drupada says that polyandry is non-Vedic:
The practice is sinful in my opinion, being opposed to both usage and the Vedas. O best of Brahmanas, nowhere have I seen many men having one wife. The illustrious ones also of former ages never had such a usage amongst them.
Now, Drupada is clearly wrong about there being no historic precedent, but he is correct that polyandry is apparently non-Vedic.
Now that there is a Vedic prohibition of polyandry, can anything override it? Consider this verse from the Manusmriti:
2.6 - The entire Veda is the root-source of Dharma, as well as the practices found in Smriti, the traditional practices of Vaidikas (AcAra), and their self-satisfaction.
Shruti (Veda) takes precedence over Smriti, which takes precedence over AcAra, which takes precedence over one's own opinion. So how can one's mother or any authority order a non-Vedic practice? If my father tells me to murder someone, then I doubt that that act becomes dharma.
Moreover, the Mimamsakas make it clear that traditional or regional customs only have authority as long as they don't conflict with the Vedas.
The Apastamba Dharma Sutra also says:
Ācārya adhīnaḥ syād anyatra patanīyebhyaḥ
He shall obey his teacher, except [when ordered to commit] sins which cause loss of caste.
From all this, I don't see how Yudhishthira's justification of polyandry is valid, unless it is the case that Smriti, AcAra, and sAdhutuSTi are on the same level as the Vedas.