How can one eliminate the psychological and nervous pressure resulting from an unwillingness to continue in the family business with one's father and grandfather, and convince the father of this, given his desire for his son to inherit this business?

If working with the father in the library does not harm the son and does not cause him to lose out on matters of his religion or worldly affairs, then it is obligatory for him to obey his father in that. However, if it causes him harm, there is no sin in leaving it and seeking another job; because obedience to parents is obligatory in matters that benefit them and do not harm the child, as Ibn Taymiyyah said. The son must be dutiful to his father and treat him well, and not cut ties with him or mistreat him. For the right of the parent is great, and being dutiful to him is among the most beloved deeds to Allah, and the Lord's pleasure is in the parent's pleasure, and His displeasure is in his displeasure, and the parent is the middle gate of Paradise.