Why does it say "va'Yhi ha'Davar ha'Zeh l'Chatas"?
Radak: Initially Yaravam did not say that it was for idolatry, rather, for Hashem. Afterwards it became a sin, for they accepted it as idolatry. From it they went to other gods, like the nations.
Malbim: Yaravam erred. He thought that just like they wanted to lighten the burden of taxes, also the burden of ascending for the festival and bringing Korbanos. Man's nature is to obligate himself in some Avodas Hashem. The harder the Avodah, the more he does it willingly. They considered it a sin that he tried to decrease their toil. They went to Dan, which is far, to get reward for each step, and not to Beis Kel, which is close!
Why does it say "Ad Dan"?
Rashi: It is at the end [of Eretz Yisrael], at the border. Radak - even so, they went to it from the other border of Eretz Yisrael, for they were such avid idolaters 1 . It says "Chei Elohecha Dan v'Chei Derech Be'er-Sheva" (Amos 8:14), for from Be'er-Sheva they would go to the god of (i.e. in) Dan, and they swore by [the idolatry].