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, is His slave and Messenger.
If you married her after her ex-husband had divorced her and her ‘Iddah (post-divorce waiting period) had expired, then she is lawfully your wife, and your children with her are lawfully attributed to you. You are not required to divorce her. You did not mention in the first question what indicates that you have done injustice to her husband, and the basic assumption is that you did not do him injustice.
As for the second question, no matter how great a sin may seem, the forgiveness of Allah, The Exalted, is greater. Whoever repents to Him, his repentance will be accepted by Allah. Allah, The Exalted, Says (what means): {Say, “O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allah. Indeed, Allah forgives all sins. Indeed, it is He Who is the Forgiving, the Merciful.”} [Quran 39:53] You should have good expectations of your Lord and beware lest Satan causes you to despair of His Mercy, which would result in your destruction.
It is forbidden to have a romantic relationship with a non-Mahram woman, and if this woman is married, the sin is graver. In addition to disobeying Allah, The Exalted, it is an offence against her husband and a violation of his honor. Part of perfecting your repentance is to seek his forgiveness and ask for his pardon, but only if you believe that it would not lead to a graver evil. If you fear it would lead to a graver evil, it is sufficient for you to supplicate in his favor and ask forgiveness for him.
We would like to stress that it is incumbent on a Muslim who is afflicted with a sin to repent and conceal his sin. He should not tell anyone of it, and he is not obliged to inform the person whom he wronged and violated his rights of what he did against him. With regard to violated financial rights, he has to return the money to the rightful owner, even if in an indirect manner. If the violated right is related to his honor or the like, he should not tell him of it but instead ask Allah, The Exalted, to forgive him and supplicate in his favor, as we mentioned above. We advise you to seek his pardon only because he already knows of your offence.
Allah Knows best.