Virata’s proposal was for Arjun not for Yudhishtir.
Despite knowing that Arjuna was not going to be the crowned king anytime in his life,Virata offered Uttara to him. He was swept off his feat by Arjuna’s extraordinary valour exhibited in Uttar go grahan battle.
Arjuna had his own reasons to refuse Uttara. He was scared of his image and he fears sin.
Arjuna knew that Guru Sishyaa relationship should not be spoilt by making his Sishyaa Uttara as his wife.
Now the next alternative that he can chose was his own son not the son of his brother.
Moreover Abhimanyu was his true successor in terms of valour and good looks. King Virat who sincerely wanted Arjun would feel satisfied if he get someone as heroic and talented as Arjuna himself.
Knowing this Arjuna prposed Abhimanyu’s name for Uttara.
Arjuna said, 'Residing in thy inner apartments, I had occasion always to behold thy daughter, and she too, alone or in company trusted me as her father. Well-versed in singing and dancing, I was liked and regarded by her, and, indeed, thy daughter always regardeth me as her protector. O king, I lived for one whole year with her though she had attained the age of puberty. Under these circumstances, thyself or other men may not without reason, entertain suspicions against her or me. Therefore, O king, myself who am pure, and have my senses under control, beg to thee, O monarch, thy daughter as my daughter-in-law. Thus do I attest her purity. There is no difference between a daughter-in-law and a daughter, as also between a son and son's own-self. By adopting this course, therefore, her purity will be proved. I am afraid of slanderous and false accusations. I accept, therefore, O king, thy daughter Uttara as my daughter-in-law. Surpassing all in knowledge of weapons, resembling a celestial youth in beauty, my son, the mighty-armed Abhimanyu is the favourite nephew of Vasudeva, the wielder of the discus. He, O king, is fit to be thy son-in-law and the husband of thy daughter.'
"Virata said, 'It behoveth the best of the Kurus, Dhananjaya, the son of Kunti, who is so virtuous and wise, to say this. O son of Pritha, do thou carry out what thou thinkest should be done after this. He that hath Arjuna for the father of his son-in-law, hath all his desires gratified.'
Arjuna clearly said that if Uttara is married to his son,her purity would not be questioned. He was apprehensive of people who may doubt his integrity.
Arjuna proudly admitted that Abhimanyu is the best in warrior skills and beauty despite being the favourite nephew of Krishna.
Virata’s approval
Virata said that he is fortunate to have Arjun as the father of his son in law Abhimanyu.
So this response of Virata proves how keen he was to have Arjun as his close relation if not as his son in law.
Prativindhya did not figure anywhere in the discussions. Neither did Yudhishtira interfere in decision making. Arjuna on his own decided the alliance.
Uttara offered to Arjuna ,got his son as her husband.
Years before the scene was different..Draupadi won by Arjuna was shared by all,with Yudhishtira’s councilling.
Uttara’s destiny differed from that of Draupadi..