How does the questioner observe the iddah after her husband divorced her with a single, first divorce at her parents' house, while she refuses to return to his home and wishes not to inform her parents of her divorce at present?

It is not permissible for a wife to abandon her husband. A woman who is revocably divorced must observe her 'iddah (waiting period) in her husband's house, and it is not permissible for her to leave it, nor is it permissible for her husband to expel her. You are obligated to return to your husband's house and observe your 'iddah there. During the 'iddah period, he is obliged to provide for you because you are considered his wife. He also has the right to take you back as long as you are within the 'iddah period. The 'iddah for a divorced woman who is not pregnant and experiences menstruation is three menstrual cycles. If she is pregnant, her 'iddah ends upon delivery. If she is one of those who do not experience menstruation, her 'iddah is three months.