Is interfering with a sister performing her household duties instead of the mother, and the ensuing problems with the sister or the mother's anger because of it, considered part of honoring one's mother, or is silence more appropriate?

The mother's right is great, and honoring her is a religious obligation. Allah has enjoined kindness to her in the Quran, and the Sunnah has allocated three-quarters of piety to her. The mother's presence is an opportunity for her children to honor and serve her and gain her satisfaction, because it is a path to Allah's satisfaction. A daughter's assistance to her mother is obligatory if the mother is in need. Whoever refuses to help, despite being able to do so, is blameworthy and neglectful. You did well by advising your sister, and you should continue advising her gently, praying, and seeking help from others. If the advice is not effective, or if her stubbornness increases, or if the mother is harmed by it, then you may remain silent.