Firstly: 

You should understand that you have a problem with regard to your religious commitment, and that is the greatest of calamities. You should also understand that the evil act of zina is one of the greatest sins that Allah forbids to His slaves and has highlighted to them its evil consequences. Allah, may He be exalted, says (interpretation of the meaning):

“And come not near to 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 Allah forgives him)”

[al-Isra’ 17:23]. 

Shaykh as-Sa‘di (may Allah have mercy on him) said: 

The prohibition on coming near to it or approaching it is more far reaching than the prohibition on merely doing it, because that includes all the things that lead to it and promote it. The one who grazes his flock around a sanctuary will soon transgress upon it, especially with regard to this matter, the inclination towards which is very strong in many people. 

Allah described zina and its abhorrent nature as a “faahishah” or great sin that is abhorrent according to sharee‘ah, reason and common sense, because it includes transgressions against the rights of Allah, the rights of the woman and the rights of her family or husband, destroys marriages, mixes lineages and leads to other negative consequences. 

The words “an evil way” means: how evil is the way of the one who dares to commit this great sin.

End quote from Tafseer as-Sa‘di, 457 

Secondly: 

Zina is a independent crime with serious consequences, and none of that sin can be erased unless you repent sincerely to Allah, may He be glorified and exalted, as Allah says (interpretation of the meaning):

“And those who invoke not any other ilah (god) along with Allah, nor kill such life as Allah has forbidden, except for just cause, nor commit illegal sexual intercourse and whoever does this shall receive the punishment.

The torment will be doubled to him on the Day of Resurrection, and he will abide therein in disgrace;

Except those who repent and believe (in Islamic Monotheism), and do righteous deeds, for those, Allah will change their sins into good deeds, and Allah is Oft-Forgiving, Most Merciful.

And whosoever repents and does righteous good deeds, then verily, he repents towards Allah with true repentance.”

[al-Furqaan 25:68-71]. 

It is not one of the conditions of sincere repentance that the zaani should marry the one with whom he committed zina; rather in order for him to marry the one with whom he committed zina, it is essential for her (and for him) to repent first, then he may marry her after that if he wishes. 

However, your sin of zina will not be any greater if her mother refuses to let her marry you nor will it be any greater if you end up not marrying one another after you both repent to Allah, may He be exalted. There is no blame on the girl or her family if she refuses to marry the one who committed zina with her because marriage, even though it may conceal the immoral actions that took place between you, is not a shar‘i remedy for the sin and shame of zina. Rather the remedy for that is sincere repentance and mending your ways – as much as you can – in the future, and doing a lot of righteous deeds, in the hope that Allah may accept your repentance.

See the answer to question no. 14381 and 11195 

Thirdly: 

Repentance does not prevent the hadd punishment from being carried out on the one who repents and it cannot be waived or reduced if proof is established against him. 

It is not one of the conditions of sound repentance that the hadd punishment be carried out in this world; rather if the sin of the sinner is found out and the hadd punishment is carried out on him in this world, that hadd punishment is expiation for him. If Allah conceals him, then the matter after that is up to Allah. 

Al-Bukhaari (17) and Muslim (3223) narrated from ‘Ubaadah ibn as-Saamit (may Allah be pleased with him, who was present at Badr and was one of the leaders on the night of al-‘Aqabah, that the Messenger of Allah (blessings and peace of Allah be upon him) said, when a group of his Companions were around him: “Swear allegiance to me on the basis that you will not associate anything with Allah, you will not steal, you will not commit zina, you will not kill your children, you will not fabricate lies against one another, you will not disobey in anything that is right and proper. Whoever among you fulfils this (oath), his reward will be due from Allah. Whoever does any of these things and is punished in this world, it will be expiation for him; whoever does any of these things then Allah conceals him, then it is up to Allah – if He wills, He will forgive him and if He wills, He will punish him.” So we swore allegiance to him on that basis. 

Ibn Rajab said:

This clearly shows that carrying out the hudood punishment is expiation for those on whom it is carried out. That was clearly stated by Sufyaan ath-Thawri, and was also stated by Ahmad, according to the report narrated from him by ‘Abdoos ibn Maalik al-‘Attaar. Ash-Shaafa‘i said: I have never heard concerning the issue that the hadd punishment is expiation anything better than the hadeeth of ‘Ubaadah.

End quote from Fath al-Baari by Ibn Rajab, 1/72 

See also Fath al-Baari by Ibn Hajar, 1/73-74 

Fourthly: 

If the hadd punishment is expiation and purification for the one on whom it is carried out, and the sinner was concealed by Allah and was not discovered, is it better for him to confess his sin to the ruler so that he may purify him by carrying out the hadd punishment on him, or is it better for him to conceal himself as Allah concealed him? 

Ibn Rajab (may Allah have mercy on him) said: 

One of them, namely Ibn Hazm, quoted as evidence this hadeeth of ‘Ubaadah to show that if a person commits a sin, it is better for him to go to the ruler and confess to him so that the hadd punishment may be carried out on him and he may thus attain expiation and not remain in the danger zone. This is based on the words, “The one who repents is subject to the divine will.” 

But the correct view is that the one who repents sincerely will definitely be forgiven. However the believer is worried about his repentance and cannot be certain that it is valid or has been accepted, so he still remains worried about his sin. 

The majority of scholars are of the view that if a person has repented from sin, it is better for him to conceal himself and not admit it to anyone; rather he should repent from it and keep the matter between him and Allah, may He be glorified and exalted. That was narrated from Abu Bakr, ‘Umar, Ibn Mas‘ood and others.

End quote from Fath al-Baari by Ibn Rajab, 1/75-77 

And there is the report which offers great hope to the one whom Allah conceals in this world. It was narrated by al-Bukhaari (2261) and Muslim (4972) from ‘Abdullah ibn ‘Umar (may Allah be pleased with him) who said: I heard the Messenger of Allah (blessings and peace of Allah be upon him) say: “Allaah will bring the believer close and will shelter him with His screen, then He will say, ‘Do you remember such and such a sin? Do you remember such and such a sin?’ and he will say, ‘Yes, O Lord,’ until He makes him confess his sins and he thinks that he is doomed. Then [Allaah] will say, ‘I concealed it for you in the world and I forgive you for it today.’ Then he will be given the book of his good deeds (hasanaat). But as for the kaafir and the hypocrite, the witnesses will say, ‘These are the ones who lied against their Lord!’ No doubt! the curse of Allaah is upon the zaalimoon (wrongdoers) [cf. Hood 11:18].’” 

And Muslim (4671) narrated from Abu Hurayrah that the Prophet (blessings and peace of Allah be upon him) said: “Allah does not conceal a person in this world but Allah will conceal him on the Day of Resurrection.” 

Let everyone feel shy before his Lord, as He has concealed him, and not disclose what He has concealed. 

Imam ash-Shaafa‘i (may Allah have mercy on him) said: 

We prefer for the one who has committed a sin that is deserving of a hadd punishment to conceal the matter and to fear Allah, may He be glorified and exalted, and not go back to disobeying Allah, for Allah, may He be glorified and exalted, accepts the repentance of His slaves. 

End quote from al-Umm, 6/149 

And Allah knows best.