Sephiroth learned that he wasn't really an Ancient, during his time in the Lifestream. This is addressed in the game, when he's confronted with the fact and acknowledges that he already knows. Jenova's his "mother" in more of a figurative or symbolic sense. The most important entity in his life, the one from whom he inherited his powers and strength, and the one he's closest to. He knows full well that she's not his mother biologically.

It was also his time in the Lifestream that gave him the knowledge the launch his plan for divinity - the Black Materia, and such.
So he has no motive. He's a plothole.
Not at all. His 'grudge against the world' was what got him started in the first place; he wanted the dominion he felt was his by right. As he learned the truth, that transformed into a willingness to sacrifice all life in order to achieve truly divine power. His motive, ultimately, is the promise of absolute power over an entire world. Pretty good motivation, especially for the progeny of a vicious and powerful being.