Should one divorce his current wife, with whom he has a marriage contract, and marry the girl with whom he committed adultery in order to cover her, or should he remain married to his first wife?

You both did well to repent to Allah from zina (fornication/adultery). The prohibition against approaching zina is more emphatic than the prohibition against committing it, and it includes the prohibition of all its preliminaries. Therefore, be careful not to be lenient in your interactions in the future. If you can marry her to treat her well and preserve her chastity, then that is good. Otherwise, hold on to your wife, strive to complete your marriage, and pray for the girl that Allah may facilitate for her a righteous husband.