An American citizen CANNOT enter the US on a foreign passport. If she renews the Chilean passport she can enter Chile on it, and then return to the US on her US passport (which she won't be allowed to leave the country without). However, the Chilean reciprocity fee is worth the life of the passport...so it might be cheaper than renewing her Chilean passport. Her husband is SOL and will pay the fee. Hope his passport doesn't expire soon!
Best,
W