Is it permissible for a legally divorced couple to divide a single apartment into two completely separate sections, each with its own private entrance, such that neither can enter the other's section except from outside the apartment, knowing that there are children and communication between the divorced couple occurs via phone or internet, and is this division limited to the iddah period or does it extend beyond that?

Each of the irrevocably divorced spouses must have an independent residence with its facilities to prevent discord. As for the revocably divorced wife, she is in the same legal position as a wife, and her husband may live with her and be in seclusion with her. It is recommended for the spouses to reconcile for the sake of the children. When children ask about the reason for the separation, wisdom should be exercised and their age taken into consideration when answering. It is permissible for a man to converse with and correspond with a non-mahram woman within the limits of Sharia and provided there is no fear of discord, especially concerning the welfare of the children or the household.