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, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
If what took place was a valid Khul’, which is a divorce in return for a compensation, then most scholars held that the husband cannot take back the wife after it except with a new marriage contract. Some scholars, however, held that the husband has the right to give back the compensation to the wife and take her back in marriage without a new contract.
Ibn Qudaamah wrote:
“There is no revocation (taking wife back) in Khul’, whether we consider it an annulment of the marriage contract or a divorce, according to the view of most scholars, including Al-Hasan, ‘Ataa', Taawoos, An-Nakhaa‘i, Ath-Thawri, Al-Awzaa‘i, Maalik, Ash-Shaafi‘i, and Is-haaq. It was narrated that Az-Zuhri and Sa‘eed ibn Al-Musayyib said, ‘The husband has the choice either to keep the compensation and (accordingly) will not have the right to take his wife back, or return it to the wife and have the right to take her back. Abu Thawr said that if the Khul’ was done with the wording of divorce, then the husband has the right to take his wife back because the right to take her back is one of the rights of divorce that is not waived by the compensation.’” [Al-Mughni, 7/331]
Based on the view of most scholars, you have been irrevocably divorced (with minor separation) from your husband with the first Khul’, and if your husband wishes to take you back, he has to conduct a new marriage contract. You do not have to wait until the ‘Iddah ends in this case because the husband may remarry his ex-wife after a Khul’ during her ‘Iddah. For more benefit, please refer to fatwas 338965and 259903.
Ibn Qudaamah wrote, “If the husband accepted the Khul’ or the marriage is annulled, he has the right to remarry her during her ‘Iddah, according to the majority of scholars of Fiqh.”
There is no objection to renewing the marriage contract in the same marital house; you do not have to inform your family or his family of it. However, it is a condition that your Wali (legal guardian) and two witnesses be present while conducting the new marriage contract. The bride's Wali cannot act as a witness in the marriage contract, but her brother can.
It is permissible for you to separate from your husband based on the first Khul’, and you must observe the ‘Iddah starting from the time you separate from him.
Allah knows best.