All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The stability of the Muslim family and the good marital relationship between the spouses is something Islamically required as well as the good relationship between the husband and his in-laws. Therefore, everybody should endeavor to achieve this objective. Allaah Says (what means): {And of His signs is that He created for you from yourselves mates that you may find tranquility in them; and He placed between you affection and mercy. Indeed in that are signs for a people who give thought.}[Quran 30:21]
If the husband's or wife's family interferes between the husband and his wife, then they should interfere with what is good and in order to reconcile between them, otherwise they should stay away.
As regards Khul’, in principle it does not take place except with the consent of both spouses. However, the Islamic judge may issue it without the presence or knowledge of the husband as we clarified in Fatwa 122890.
Since this Khul’ took place by an Islamic court, then we cannot say anything about it. If you have grounds to appeal it, then you may do so in an Islamic court. However, if you have no grounds to appeal it, then you have to accept the matter.
In any case, Khul’ takes place as one irrevocable divorce according to the most preponderant opinion of the scholars as clarified in Fatwa 88502. Therefore, you cannot take your wife back except with a new contract and a new dowry and with the consent and presence of her guardian and two witnesses. As regards the presence of the marriage registrar, then this is not a condition for the validity of the marriage contract.
In order to convince her and her family, you should first of all seek the help of Allaah, and then the help of some rational people (who may influence them).
Finally, you should know that a separate accommodation is a right of your wife over you, and she is not obligated to reside with your family in one accommodation. For more benefit, please refer to Fatwa 84068.
Allaah Knows best.