Is a girl's refusal to marry her cousin, despite her mother's insistence and threat of not forgiving her, considered an act of disobedience that prevents her prayers from being answered?

The mother does not have the right to force her daughter to marry someone she does not desire. The daughter's disobedience to her mother in this matter is not an act of disrespect (uquq) and does not prevent the acceptance of prayers. As Ibn Taymiyyah mentioned, parents cannot compel their child to marry someone they do not want, and if the child refuses, they are not considered disobedient. This is because disliking an unwanted marriage is more severe than disliking food. The daughter must strive to be dutiful to her mother and treat her kindly.