Is it permissible for the wife to take money from her husband without his permission to educate their son and help him memorize the Qur'an, or for any hardship, in the event that the husband does not fall short in spending but does not have a specific goal for his son?

If your husband does not fall short in his duties towards you, then he will most likely not fall short in educating his son. It is not permissible for you to take his money without his knowledge and permission under the pretext that he does not see a goal for his son. You must reach an understanding with him regarding the best interest of your son, and it is not lawful for you to take anything from his money without his knowledge unless you fear the occurrence of hardship.