Part 1

Sean, as a former Jesuit and ardent follower of Ignatian spirituality, please allow me to add a few facts to you vague allusions to Jesuit obedience.

Reference to Jesuits’ special obedience to the episcopal magisterium are generally two fold: (1) some Jesuits take a fourth vow (beyond poverty, chastity and obedience) of obedience to the pope with regard to mission, and (2) there is an appendix in the Spiritual Exercises of Ignatius entitled "Rules for Thinking with the Church." 

IMHO, Pope Francis, the first Jesuit pope, has quietly but dramatically illustrated how this obedience ought to be practiced today. 

FIRST, let's look at the "Rules for thinking with the Church." The full text can be found here:
http://www.sacred-texts.com/chr/seil/seil82.htm