Is the behavior of the questioner and her sisters considered disobedience or a sin, based on the treatment they receive from their mother who abuses, humiliates, and deprives them of food and medical treatment despite having money, knowing that the father is not responsible for them?

Abusing or wronging by parents does not negate their right over their children. Allah has commanded kind companionship towards مشرِكين (polytheist) parents. Imam Bukhari dedicated a chapter titled "Filial Piety Towards Parents Even If They Wrong" and included under it a narration from Ibn Abbas that confirms this. The mother's right is more emphasized than the father's. Therefore, you must be dutiful to them, be patient with them, and be careful not to offend them. If a slip occurs within the scope of Allah's forgiveness, then Allah is Oft-Forgiving to those who repeatedly turn to Him. The financial support of needy children is incumbent upon the father. Concealing marriage to obtain a pension is deception and illicitly consuming wealth.