Complex sentence: The orthodox synagogues refused to allow Malavsky to appear together with his daughters; on the other hand, Malavsky refused to accept a cantorial appointment in a conservative synagogue, finding the changes to update the liturgy unacceptable.
Split into simpler sentences: The Orthodox synagogues refused to allow Malavsky to appear together with his daughters. On the other hand, Malavsky refused to accept a cantorial appointment in a Conservative synagogue, finding the changes to update the liturgy unacceptable.