He married a second wife and they became Muslim – what should he do with his first wife?
Question

I would appreciate if you can give an immediate answer to this question which has been bothering my new brother who just professes his faith in Islam.  
A man has had a relationship with a woman bearing 2 children during their marriage relationship way back on their own country. In the course of time, the man got a job in Saudi Arabia for contractual basis, leaving his wife and children behind. At the time the man was working in Saudi Arabia, he met a woman and had a relationship with her which bores them 1 child. A civil marriage ceremony was consumated without the knowledge of the first wife which he leave in his own country.  
Now, the couple who both works in Saudi Arabia recently embraced Islam. Since both are new in the religion, fearing they might commit sins/wrongs which is against the teaching of Islam, could you please give us your advise on the following:  
1. what is the Islamic ruling about the relationship mentioned?  
2. what is the man's responsibility as far as to his 2 children from the first wife, and what is his responsibility now to the first wife?  
3. what sins are committed and what to do to avoid this sins?   Further, please give Islmaic advice as regards the siutation stated above.
Praise be to Allah.Firstly: 
We praise Allaah for having guided them to Islam, and we ask Allaah to make them steadfast in Islam until death, so that they may attain the Paradise of Allaah and His good pleasure. We give them the glad tidings that Islam erases whatever sin came before it. No matter what sins a person may have committed, if Allaah then blesses him with guidance to Islam, then he will become cleansed and free from sin as on the day his mother bore him. Allaah says (interpretation of the meaning): 
“Say to those who have disbelieved, if they cease (from disbelief), their past will be forgiven”
[al-Anfaal 8:38]
“If they cease” means if they give up their kufr or disbelief by submitting to Allaah alone, with no partner or associate. Tafseer al-Sa’di. 
The Prophet (peace and blessings of Allaah be upon him) said: “Islam erases whatever came before it” (narrated by Muslim, 121) – meaning, of sin. 
Secondly: 
A man does not have the right to form a relationship with a woman who is a stranger (non-mahram) to him. If something of that nature happened before they got married, it is a sin which is recorded against them. If that happened before they became Muslim, then Allaah has forgiven it when they became Muslim. 
If that happened after they became Muslim, then they have to repent from that. Allaah has promised to accept the repentance of the one who turns to Him in repentance. He says (interpretation of the meaning): 
“And He it is Who accepts repentance from His slaves, and forgives sins, and He knows what you do”
[al-Shoora 42:25]
“But indeed, I am the Perpetual Forgiver of whoever repents and believes and does righteousness and then continues in guidance.”
[Ta-Ha 20:82]
For more information on repentance and its conditions, please see question no. 13990. 
Thirdly: 
There is no sin involved in a man’s marrying a second wife. Allaah has permitted a man to have up to four wives, if he is able to treat them fairly and give them all their rights. He does not have to inform his first wife of his desire to marry a second or that he has already done so. 
Fourthly: 
With regard to the man's duties towards his children and first wife, he has to spend on them according to their needs. What really matters is that he should try to guide them and save them from the Fire, as Allaah says (interpretation of the meaning): 
“O you who believe! Ward off yourselves and your families against a Fire (Hell) whose fuel is men and stones, over which are (appointed) angels stern (and) severe, who disobey not, (from executing) the Commands they receive from Allaah, but do that which they are commanded”
[al-Tahreem 66:6]
So he must do all that he can to call his wife to Islam and to advise her, and encourage her to embrace Islam. If she refuses then he can still remain married to her and not divorce her if she is from among the People of the Book (i.e., Jewish or Christian). But if she is an idol-worshipper then it is not permissible for her to remain the wife of a Muslim, so in that case he has to divorce her. 
Please see also question no. 9949. 
It should be noted that if one of the parents becomes Muslim and his children are still small (i.e., below the age of adolescence), then they are judged to be Muslim because of his becoming Muslim. But if they are adults or have reached the age of adolescence, then that is not the case. See al-Mughni, 13/115; Ahkaam Ahl al-Dhimmah by Ibn al-Qayyim, 2/507. 
Based on this, if the small children know that Allaah has blessed him and them with guidance to the true religion, then he has to teach them about tahaarah (purity, i.e., wudoo’) and prayer, and other rulings, so that they will grow up with it and get used to doing it, following the command of the Prophet (peace and blessings of Allaah be upon him): “Teach your children to pray when they are seven years old and smack them if they do not do it when they are ten, and separate them in their beds.”
Narrated by Abu Dawood, 495; classed as saheeh by Shaykh al-Albaani in Saheeh al-Jaami’, 5868. 
See also question no. 10016. 
He should not stay here for work and leave his young children exposed to loss and deviation; he should try to bring them here to be with him, so that he will be able to do that which Allaah has enjoined him to do of bringing them up well. If he cannot bring them here then he should be in constant contact with them, corresponding with them and guiding them. It is not permissible for him to neglect them and leave them to be lost. He will be responsible for them on the Day of Resurrection.  
We also encourage our new brother and his wife to learn the rulings of Islam by reading and asking knowledgeable people and reading useful Islamic sites on the internet, and to apply whatever they have learned in the required manner. 
We ask Allaah to make them steadfast and help them to do that which He loves and which pleases Him. 
And Allaah knows best.