They were in a haraam relationship then they repented and got married without a wali (guardian); what should they do now?

Firstly: 

We ask Allaah to accept your repentance and to forgive you, and to help you to obey Him and worship Him well. 

Secondly: 

Your marriage contract without the approval of the wife’s guardian is invalid, and you have to renew it in the presence of the guardian. If he cannot attend then he should appoint someone to do the marriage contract on his behalf. 

It was narrated that Abu Moosa (may Allaah be pleased with him) said: The Prophet (peace and blessings of Allaah be upon him) said: “There is no marriage except with a wali (guardian).” Narrated by al-Tirmidhi (1101), Abu Dawood (2085) and Ibn Majaah (1881); classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.

Shaykh al-Islam Ibn Taymiyah said: 

The majority of scholars said that a marriage done without a guardian is invalid, and they ruled that a ta’zeer punishment should be carried out on the one who does that, following the example of ‘Umar ibn al-Khattaab (may Allaah be pleased with him). This is the view of al-Shaafa’i. A number of them also suggested that the hadd punishment of stoning should be carried out in such cases and others. End quote. 

Majmoo’ al-Fataawa (32/21). 

He also said: 

The Qur’aan indicates this in more than one place, as does the Sunnah in more that one place, and it was the habit of the Sahaabah. Women can only be given in marriage by men, and it is not known that any woman gave herself in marriage. This is what distinguishes between marriage and illicit relationships. Hence ‘Aa’ishah said: No woman should give herself in marriage, for the prostitute is the one who gives herself in marriage. End quote. 

Majmoo’ al-Fataawa (32/131). 

The author of ‘Awn al-Ma’bood (6/101) said: 

In fact marriage without a guardian is invalid, as is indicated by the hadeeth. End quote. 

What you must do now, if you want to set things straight and make your marriage in accordance with sharee’ah, is to do the marriage contract again, in the presence of the wife’s guardian and with his approval.  

It should be noted that you must hasten to set this matter straight, because your staying together now is haraam, because the marriage contract that was done between you before was not valid. 

In order to expedite matters, you can contact her father by phone and he can say to you: “I give my daughter So and so to you in marriage” and you can say, “I accept,” and that should be done in the presence of two witnesses who know the father’s voice and can hear him.

Thirdly: 

With regard to the children, they should be attributed to you because you did the marriage contract without a guardian thinking that it was valid. 

And Allaah knows best.