Does a sister's pursuit of a master's and doctorate degree—so she doesn't feel inferior to her diligent sister—constitute a challenge to divine decree? Will she be rewarded for her endeavor to become a university professor, or is this a worldly pursuit for which she will be punished?

Your diligence in studying, your pursuit of excellence, and your aspiration to obtain a doctorate are not blameworthy; rather, they are among the righteous matters that Allah loves. You should be content with what Allah has chosen for you, while still having ambition and striving for the best, and this is not an objection to divine decree. However, competition and envy over worldly matters are not befitting a Muslim. It is better to look at those who are less fortunate in worldly affairs to appreciate blessings. As for true competition, it should be in matters of the Hereafter, by looking at those who are more obedient to Allah and striving to surpass them, in accordance with His Almighty saying: "And for that let the competitors compete." Therefore, you should put matters in their proper perspective.