If a holy couple is in love, and is having a child on the way and wants to bring the child in right, but one of the mates parents does not agree with a marriage so young. So the couple brings their relationship to God because they both have strong relationship with Him. And they make their relation a covenant relationship, (basically what a marriage is) and they give each other wedding rings and everything. Are they married in God's eyes, because they made a covenant with God, and covenants are strong promises.
There are several problems in what you propose. You claim that the young couple are "holy" and that "they both have a strong relationship with" God, yet in the scenario you describe they have been sinning, since they have a child on the way. This means they have been committing fornication.
"This is the message which we have heard from Him and declare to you, that God is light and in Him is no darkness at all. If we say that we have fellowship with Him, and walk in darkness, we lie and do not practice the truth" (I John 1:5-6). To walk in darkness is to live a life where you are committing sin. Thus, despite your claim, God says this couple out of fellowship with Him because of their sins. "But your iniquities have separated you from your God; and your sins have hidden His face from you, so that He will not hear" (Isaiah 59:2).
One of the things that also becomes a sin is when people purposely mix right and wrong. "Woe to those who call evil good, and good evil; who put darkness for light, and light for darkness; who put bitter for sweet, and sweet for bitter! Woe to those who are wise in their own eyes, and prudent in their own sight!" (Isaiah 5:20-21). Ancient Israel had this problem and it seems that it continues today. So let's not dress this sinful couple up in sweet sounding words.
Now, despite God's clear warnings not to do it, this couple has been having sex and claiming to be in love with each other. This is not love! It is selfish gratification of bodily desire. Love "thinks no evil" (I Corinthians 13:5), but this couple has been committing fornication. Now an innocent child is on the way to two immature people who only think about their sensual desires. Since he is so young, does he have a job to support a wife and a child? Can he provide food, shelter, clothing to those he has made dependent on him? Most likely no. "But if anyone does not provide for his own, and especially for those of his household, he has denied the faith and is worse than an unbeliever" (I Timothy 5:8).
But now this couple who has been flaunting God's Law suddenly wants to drag God into the middle of the mess that they have made and declare to God that they are going to true to each other after proving they won't be true to God. There is much more to making a covenant than just an exchange of promises. One of the reasons we hold weddings in ceremonies is because a covenant requires witnesses to the vows. By being there these people are indicating they will do what they can to uphold that covenant.
Okay, so one set of parents say that the couple is too immature and irresponsible for marriage. They have a point. They demonstrated that they are unable to restrain their basic desires for even a short while. They made a child without thinking about the future. How is any of this giving confidence to the parents that they really are ready for adult responsibilities?
What needs to be done is:
- They need to quit having sex. They need to repent of their sins and humbly ask God for forgiveness.
- Assuming they will marry when they get old enough, she needs to start making preparations for the care of the child. Hopefully her parents will allow her to continue to live with them and help her learn how to be a mother.
- Meanwhile, he needs to get working to support the girl and his child. He caused it, he should own up to his responsibilities. That means paying for her doctor bills, food bills, clothing bills, and whatever is needed for the child when he is born. He needs to make arrangements for a place that they can live after they are old enough to marry. And if he proves himself to be a responsible young man who is a consistent provider, who knows, the parents might agree that they don't have to wait so long to get married.