I'm an Arab living in Japan and I'm married to a Japanese woman. She is Muslim and I have 3 children from her but I always have problem with her about our sex relation as she doesn't like to have this kind of relation with me when I need. Sometimes I commit Zina (adultery). Now I want to get married in another country to never get in Zina any more but my father and mother does not accept that. Even the law in my country doesn't accept to give me the certificate for getting married.
So if I get married just in front of the Imaam with my new wife's family, in the future, if I will have a child, I can't give them my name and they have to take the mother's name or the mother's father's name. Please advise me to resolve this problem to get out of Zina problem.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

First of all you have to sincerely repent to Allaah for that great major sin that you had committed. Indeed, adultery is one of the greatest major sins and Allaah warned us against it in His book saying (which means): {And come not near the unlawful sexual intercourse. Verily it is a fahishah (i.e. anything that transgresses its limits; a great sin) and an evil way (that leads one to Hell) unless Allaah forgives him/her.}[Qur'an 17:32] Therefore, whoever has committed such a sin has to sincerely repent to Allaah fulfilling the conditions of a true repentance; for details refer to Fataawa: 87903 and 83611.

Besides, you are required to conceal your sin and not reveal it to anyone, as the Prophet said: "Avoid such filthy things which Allaah has forbidden (sins), and whoever was involved in any of them, has to conceal himself and repent to Allaah because if one reveals his sin to us, we have to apply the punishment on him.'' [Al-Haakim]

Your wife has also to repent to Allaah for her disobedience to you and not responding to you when you call her to bed. By refusing to accept her husband's request, she might be the reason that led you to commit adultery. It is confirmed that the Prophet said: "If a woman spends the night away from her husband's bed [voluntarily refusing to share the bed with him], the angels will curse her till the morning." [Ahmad]

Another narration reads: "If a husband calls his wife to bed (to have sexual intercourse with her) and she refuses, and he spends the night angry with her, the angels would curse her until she gets up in the morning." [At-Tabaraani]

Another narration further reads: "If a husband calls his wife (to have sex with her) then she must respond even if she were (working) at the furnace." [At-Tirmithi]

So she has to repent to Allaah from her sin and obey her husband whenever he calls her to bed as this is one of his greatest rights on her.

With regard to other matters that you have mentioned that the country does not allow more than one wife and does not issue documents if married to a second wife and thereby the children are not traced to their father, then all of this is a result of staying and living with non-Muslims. The Prophet warned us against living in non-Muslim countries as he said: "Whoever lives and dwells with a non-Muslim, he is like him." [Abu Daawood] The Prophet also said: "I am innocent from any Muslim who resides among the non-Muslims." The companions asked: "Why is it so, O Prophet of Allaah?" He replied: "The fire of Muslims should not be seen with the fire of disbelievers [non-Muslims] (i.e. they should be so far that they can not see each others fire)."

The solution to this problem is to leave those countries whose citizens wrong themselves by associating partners with Allaah and commit all kinds of sins. It is better for a Muslim to live in his country where he can perform his religious rites and obligations though facing some financial difficulties, rather than living in non-Muslim countries, committing adultery (and other kinds of sins) even if he owns a kingdom similar to that of Qaaroon (Kirah). Hence, you have to fear Allaah and have consciousness that He is always watching you, because life is but few days. So you should put priority on the next life over this temporary life, and Allaah says (which means): {And whoever fears Allaah-He will make for him a way out. And will provide for him from where he does not expect.}[Qur'an 65:2-3] 

Allaah knows best.