Is the mockery and insult from one's family when prayer is prolonged, and their claim that the girl is "deficient in intellect," a justification for her desire to marry a specific person and become attached to him?

Your family is doing wrong by ridiculing you, so command them to fear Allah and to be an aid to you in obedience. You must be patient and advise them to desist from this behavior. Occupy yourself with beneficial knowledge and useful skills, and do not escape into the illusions of love and infatuation. Seek help from Allah, and rectify your affairs. If your heart inclines towards a righteous man, it is permissible to propose marriage to him within the prescribed Islamic guidelines.