Is it valid and acceptable to supplicate for Allah to unite a young man and a young woman as a married couple, according to the Book of Allah and the Sunnah of His Messenger, with the knowledge and consent of their families, and given a prior relationship between them?

As long as you know that these relationships are forbidden, you must end them immediately and repent to Allah. Your persistence in them exposes you to Allah's wrath. It is not permissible for you both to continue in this sin under the pretext of family knowledge or the desire for marriage. There is no harm in supplicating for ease in marriage, and the matter of

the supplication's acceptance rests with Allah, but be certain that Allah decrees nothing but good for His believing servant. Remember that sins can be a reason for supplications not being answered.