Is it permissible to marry a girl with whom the questioner committed adultery, then divorce her to cover her, knowing that she is not committed [to religious observance] and will travel to non-Islamic countries and will not wear the hijab there, despite his love for her and his certainty of her sincerity?

You must repent from committing the indecency, regret it, and ask Allah for pardon and forgiveness. Your marriage to the girl is required if your repentance is sincere; otherwise, it is not permissible according to the preponderant opinion. Therefore, the marriage of a chaste person to an unchaste person, or the marriage of a chaste woman to a profligate man, is not valid until they both repent with a sincere repentance.