Is it obligatory for the questioner to continue working with his father in the contracting business, which is tainted by corruption, or should he look for another job or leave the house?

Your father is not permitted to compel you to commit acts of disobedience (to Allah), and it is not lawful for you to obey him in such matters. However, if he wishes for you to partner with him in work, then obey him and try to establish things in a way that pleases Allah. If you strongly believe that you will not be able to remain steadfast (in righteousness), then do not agree to partner with him. Refuse gently, explaining the reason, and clarify that if he were to change his unlawful methods, he would find you obedient. Regarding your relationship with him, advise him with wisdom, not harshness. If he does not respond, his guidance is not your responsibility. Do not leave the house as long as he needs you, especially since you are his eldest son, unless your continued presence leads to committing forbidden acts. In that case, you may leave, while still maintaining good companionship with him and fulfilling his rights.