Complex sentence: Things are a little tense between Chapin and Liza due to a fight they had days earlier, and won't be "down" until Liza apologizes--which Liza refuses to do.
Split into simpler sentences: Things are a little tense with Chapin and Liza due to a fight they had days earlier. And won't be "down" until Liza apologizes which Liza refuses to do.