Is it permissible for a second wife, who has returned to her husband after her first divorce, to waive her material rights (the apartment) that her family had previously guaranteed for her, fearing a repeat of the divorce experience, especially since both her parents are deceased and she has no siblings?

If the divorce is revocable (talaq (definition) raj'i), the husband has the right to take his wife back without her permission as long as she is within her waiting period (iddah (definition)), and her family does not have the right to prevent their daughter from this. Regarding his condition of waiving the apartment for him to take you back, the majority of jurists do not consider a revocable return (raj'ah) that is contingent on a condition to be valid. However, if the revocable return is valid without a condition, and the waiver was a promise from you or from him, then the return is valid. It is advised not to waive the apartment, in order to preserve your right. If the husband is sincere in his desire to take you back, he will do so without a condition, as many husbands are deterred from divorce by financial burdens, and waiving the apartment will make it easier for him to divorce in the future.