All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Sodomy is a heinous practice and a grave sin. The Islamic Shariah prescribed a severe punishment for it in the life of this world, which is to kill both perpetrators, and a severe punishment in the Hereafter, which is the fire of Hell and wretched settlement in it. Please refer to fatwa 335338.
It is incumbent on you to hasten to repentance without any procrastination; you do not know when your life will end. Death may take you by surprise, and you would then meet your Lord before repentance and regret this at a time when regret will be of no avail; Allah, the Exalted, says (what means): {The repentance accepted by Allah is only for those who do wrong in ignorance (or carelessness) and then repent soon after. It is those to whom Allah will turn in forgiveness, and Allah is ever Knowing and Wise.} [Quran 4:17] Please refer to the conditions of repentance in fatwa 86527.
In addition to repentance, you are required to conceal your sins; disclosing one's sins is itself a sin. Abu Hurayrah, may Allah be pleased with him, narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said, "All my followers are safe, except those who sin openly or disclose their sins. An example of such disclosure is that a person commits a sin at night, and though Allah screens it from the people, he comes in the morning and says, 'O so-and-so, I did such-and-such last night.' He spent his night screened by his Lord (none knowing about his sin), and in the morning he removes the screen of Allah from himself." [Al-Bukhaari and Muslim]
Thus, you realize that you did wrong by informing your wife of your sin and by informing your mother and sister. You must not inform anyone else, and if you are asked about it, you should resort to Tawriyah (deliberate ambiguity; i.e. to say something which has more than one meaning and intend a meaning different from what the listener is likely to understand). You may deny that you did that while intending that you did not do it after your repentance. ʻUmar, may Allah be pleased with him, said, "Deliberate ambiguity is a safe way to avoid lying." [Al-Adab Al-Mufrad]
You are not required to offer expiation along with your repentance (you are not required to fast two months or feed 60 poor people).
It is hoped that your repentance would be the means for saving your marriage; otherwise, if you do not change, your wife has the right to ask for divorce. The Hanbali scholar Al-Buhooti wrote, "If the husband neglects any of the rights of Allah, it is recommended for the wife – just as it is recommended for the husband in a similar situation – to request termination of the marriage through divorce or Khulʻ (divorce at the instance of the wife in return for a compensation payable by her) for his neglect of the rights of Allah upon him."
The matter is simple; if you have strong willpower and sincere determination to repent, Allah, the Exalted, will guide you to repentance. If you are true to Allah, Allah will be true to you. He says (what means): {And when the matter (of fighting) was determined, if they had been true to Allah, it would have been better for them.} [Quran 47:21] Moreover, the Prophet, sallallaahu ‘alayhi wa sallam, said to one of his Companions, "If you are sincere towards Allah, Allah will fulfill your wish." [An-Nasaa’i]
Lastly, we would like to point out that if living abroad makes you more vulnerable to temptation and makes committing this sin easier, then it is incumbent on you to leave, so go back to your country to guard your chastity and your wife's. For more benefit, please refer to fatwa 86405.
Allah knows best.