So that the sovereignty was divided and a disobedient kingdom arose out of Ephraim: Ephraim refers to the northern kingdom, the group of Israelite tribes that separated from the tribe of Judah and its royal line after the death of Solomon. The sovereignty was divided refers to that separation. “It [Solomon’s foolish behavior] divided the nation” (Good News Translation). Disobedient kingdom refers to the fact that the new kingdom in the north did not recognize the authority of the royal line of David, which remained in control of Judah to the south. Good News Translation “rival kingdom” is a reasonable way to say this. New English Bible has “rebel kingdom,” which may be better, but we may use a verb here; for example, the whole verse may be rendered:

• Because of your foolishness, the people in the north broke away [or, rebelled], dividing Israel.

Quoted with permission from Bullard, Roger A. and Hatton, Howard A. A Handbook on Sirach. (UBS Helps for Translators). New York: UBS, 2008. For this and other handbooks for translators see here.