Was the divorce of the aforementioned woman from her first husband lawful and valid, and is there any sin for her refusal to return to him, and how can she repent now that she is married to another man?

If a man divorces his wife with the first or second pronouncement, it is a revocable divorce, and he has the right to take her back as long as she is within her waiting period (iddah (definition)), without requiring her consent, because a revocably divorced woman is considered to be like a wife. If the waiting period expires without him taking her back, then a final separation has occurred, and the woman is permitted to marry someone else. There is no sin upon the divorced woman for refusing to return if her husband gave her a choice and did not force her to return. However, if she acted in a way that prevented him from returning to her without a valid reason, then she must seek forgiveness. Now, the focus should be on making the new husband happy and establishing a successful marital life.