Is joining the Islamic Academy considered disobedience to the mother and a sin if the mother is displeased with it out of fear for her daughter's studies, even though the daughter believes she can reconcile the two?

If the academy is in the same city, there is no harm in joining it despite your mother's refusal, as her permission is not required for seeking knowledge in urban areas, and her obedience is not obligatory in abandoning it. Imam Ahmad issued a fatwa stating that parents are not to be obeyed if they forbid seeking beneficial knowledge. The student should try to appease and please them as much as possible without abandoning the pursuit of knowledge, and this is not considered disobedience.