Dear user, we explained all the probable suppositions concerning divorce in our previous answer to your question (No.6795). We see that you have not stated whether or not you had complete martial relations with your husband. If you had sexual intercourse with your husband and then you got Khula divorce  , the man cannot rejoin you without a fresh marriage contract insofar as you have not taken back the property which you had surrendered to him in lieu of the divorce. If you did not know the Islamic law and you committed sexual intercourse due to ignorace, waty bish-shubha (intercourse by mistake) has taken place. Your second marriage (after keeping the Iddah of waty bish-shubha) is correct because it had been after Khula divorce. However, if you took back the property (or money) which you had surrendered to him and then you continued your relations with your husband, you should get a divorce from your first husband and then contract marriage with another man. If he did not divorce you, you are still considered to be his wife according to Islamic Shari'ah and the second marriage is invalid. If you did not get a divorce from your first husband, you cannot contract marriage with another man.
For your confidence, we asked His Eminence, Ayatollah Mahdi Hadavi Tehrani to reply to your question which you can read for yourself.
The answer given to your question by Ayatollah Mahdi Hadavi Tehrani is as under:
1. Talaq Khula is "Talaq Bayin" (irrevocable divorce) and it is not possible for the husband to return to his wife during Iddah (waiting period) except for when the wife takes back what she had given him for the divorce in which case the man can rejoin his wife and there is no objection in it.
If the sexual intercourse after the year 2003 (following the Khula divorce) had been without the woman taking back the surrendered property, the man's return is invalid and the woman is considered as divorced. The new marriage contract is in order. In case, the intimate relations take place after the woman's taking back the surrendered property, the return (rejoining) is in order and the woman is considered to be the first man's wife and the new marriage contract is void.
For further information, see the following indexes:
1. Index: Khula divorce, question 5849, (site: 6059)
2. Index: Divorce through
question No.376, (site: 387)
 - A woman who develops an aversion from husband and is not willing to live with him and there is fear that the continuation of their marriage life would lead to committing sin, can surrender to him her dower or other property so that her husband may divorce her. This divorce is called ‘Khula’ divorce’.