About the one year theory. This is an expert from kmg about picnic that govind and parth planned after arjuna s return from 12 months of exile. Drapaudi and subdhara accompanied. Them
Here-
After a few days, Vibhatsu, addressing Krishna, said, 'The summer days have set in, O Krishna! Therefore, let us go to the banks of the Yamuna. O slayer of Madhu, sporting there in the company of friends, we will, O Janardana, return in the evening'. Thereupon Vasudeva said, 'O son of Kunti, this is also my wish. Let us, O Partha, sport in the waters as we please, in the company of friends.' "Vaisampayana continued, 'Then, O Bharata, having consulted thus with each other, Partha and Govinda, with Yudhishthira's leave, set out, surrounded by friends. Reaching a fine spot (on the banks he Yamuna) suitable for purposes of pleasure, overgrown with numerous tall trees and covered with several high mansions that made the place look like the celestial city and within which had been collected for Krishna and Partha numerous costly and well-flavoured viands and drinks and other articles of enjoyment and floral wreaths and various perfumes, the party entered without delay the inner apartments adorned with many precious gems of pure rays. Entering those apartments, everybody, O Bharata, began to sport, according to his pleasure. The women of the party, all of full rotund hips and deep bosoms and handsome eyes, and gait unsteady with wine began to sport there at the command of Krishna and Partha. Some amongst the women sported as they liked in the woods, some in the waters, and some within the mansions, as directed by Partha and Govinda. Draupadi and Subhadra, exhilarated with wine, began to give away unto the women so sporting, their costly robes and ornaments. And some amongst those women p. 434 began to dance in joy, and some began to sing; and some amongst them began to laugh and jest, and some to drink excellent wines. Some began to obstruct one another's progress and some to fight with one another, and to discourse with one another in private. Those mansions and the woods, filled with the charming music of flutes and guitars and kettledrums, became the scene of Prosperity personified
Note that here drapaudi os found in arjuna s company so probably it was his year .
And immediately after the khandav dahan after they came back to ip it is said that yudhishtra dismissed everyone to spent some lone time with drapaudi how come yudhishtra got to spend quality time with drapaudi in arjuna or at most nakula s year
Meanwhile king Yudhishthira of unfading glory, accompanied by his brothers and surrounded by friends, entered his excellent capital. And that tiger among men, dismissing all his relatives, brothers, and sons, sought to make himself happy in the company of Draupadi. And Kesava also, worshipped by the principal Yadavas including Ugrasena, entered with a happy heart his own excellent city. And worshipping his old father and his illustrious mother, and saluting (his brother) Valadeva, he of eyes like lotus-petals took his seat. Embracing Pradyumna, Shamva, Nishatha, Charudeshna, Gada, Aniruddha and Bhanu, and obtaining the leave of all the elderly men, Janardana entered the apartments of Rukmini."
This kind of dismisses that one year rule once for all. And further strengthen that only yudhishtra was married to Krishnaa