1)
What is the meaning of "va'Yigel"?
1.
Rashi: Since there is Chirik under the Yud, it is an expression of being exiled, and not of exiling others.
2)
Why did Hashem exile them when He did?
1.
Malbim: He saw that there is no other solution. Yehudah was different; they sinned inadvertently, through seeing the deeds of Yisrael. When Yisrael are exiled, Yehudah will not have from whom to learn [evil]!