Am I entitled to claim my apartments in Cairo and Hurghada, and the list of movable assets, in exchange for leaving the Alexandria apartment, gold, gifts, and the car to my wife, while covering the children's expenses, given that I was subjected to verbal and financial exploitation, and I fear the impact of court proceedings on the children?

A wife's removal of the hijab (definition) is a grave sin. It is obligatory to prevent her from doing so and to compel her to wear it when going out or appearing before non-mahram (definition) men. Her request for divorce is justified if there is a valid reason, such as severe beating or wrongful abuse, and in such a case, you are not entitled to demand that she waive her rights. However, if her request for divorce is without a valid reason, then you have the right to refuse divorcing her until she redeems herself from you with her wealth. It is recommended that you do not take from her more than her mahr.