An interesting point is that Vidura is called one with many excellent and best sons. He is also avatar of son of Atri.
Vidura is listed as Avatar of Dharma who is son of Atri.
Dharma originally was born as son of Brahma. Later Yamaraja took that title as Dharmaraja Yamaraja the son of Vivasvana (one of the sun god).
Here we have a third Dharma, son of Atri.
Later Aryama, the Aditya became Dharma and was father to Yudhishthara. The three tests of Dharmaraja were conducted by Three Dharmadevas, the Kanka or Aryama, the Dog Sarameya or son of Atri and finally by Brahma Dharma himself in increasing level of complexity.
So here Dharma, son of Atri is interesting.
Neelkantha in his commentary thinks the Atri here in Mahabharata Anshavtara period should be replaced with Surya.
BORI also thought they may find a text of Mahabharata which says Surya and not Atri. They could not.
The sloka in Critical edition also states Atri. The commentator was of opinion that Atri was one of fourteen Suns. Again, that does not make Dharma Yama the son of Vivasvana, son of Atri in any scenario.
Atri is name for Siva also in same set of texts.
Now Atri is great, he is a Saptarishi, a Chitra Shikhandi, his son Dattatreya is avatar of Vishnu, another son is Prachinbarhi (the ancient fire) whose ten sons are Prachetas.
He once assumed the role of both Sun and Moon because of Devasura sangrama caused the original gods to fade away. (Actually, this story is told by Bhima to Arjuna).
Atri is ancestor to Janaka and hence to Sita.
The Brahmanada Purana sheds a light. It is one of the Khila Puranas aka appendix to Mahabharata.
The AniMandavya story
The story goes when AniMandavya Rishi was put on the stake by mistake by King’s guards. He was in great pain but not dying. He was waiting for sun to rise, so he can talk to King and prove his innocence.
Atri Muni’s son Ugrasravas was the husband of Silavati. No other woman had so far surpassed Silavati in her fidelity to her husband.
Once, Ugrasravas happened to fall ill. He expressed his desire to visit a nagar vadhu’s house. As he was too weak he could not walk. The devoted wife Silavati carried him on her own shoulders and took him to the nagar vadhu’s house.
Now, they were passing near the place where Ani Mandavya was lying on the stake and in considerable pain. But even he was surprised by the tableau of wife carrying her sick husband. He asked the lady why she is carrying her husband. She told him of the wishes of her husband.
Mandavya was flabbergasted. Anyway the stake was flabbering his gast anyway. He was in pain and said “I am put on stake and Atri’s son wants to visit the Nagar Vadhu in his illness.”
“I curse that Ugrasrvas will die before sunrise.”
Hearing it Silavati said “Sun will not even rise.”
Stating so, she took her husband to his desired place.
The sun did not rise, could not rise. The whole of nature came to standstill. The solution was to persuade Silavati. Her tapobala was keeping Sun down.
The Gods requested Atri’s wife Anusuya, the mother-in-law to persuade Silavati. This was a great test for Anusuya as well. She is asking her daughter in law to withdraw her curse that will kill her own son. But whole nature was in trouble. She convinced Silavati. The sun rose and Ugrasrva died.
Next day, the King freed Ani Mandavya who cursed Dharma to be born as Vidura. To reward Anasuya who sacrificed her son, Brahma was born as Soma, Siva as Durvasa and Vishnu as Dattatreya. She later also gave a lesson to her own descendant Sita, descended through Dattatreya.