Complex sentence: Israel appears to have used the non-accession method, while Judah used the accession method until Athaliah seized power in Judah, when Israel's non-accession method appears to have been adopted in Judah.
Split into simpler sentences: Israel appears to have used the non-accession method, while Judah used the accession method. It also appears that Judah adopted Israel's non-accession method during the time when Athaliah seized power in Judah.