How to deal with a narcissistic sibling?

This aspect of my parent's care bothers me more than it should. Myself and my younger sister have POA and FPOA for our parents. Since their health has been declining, we have been working together to be in charge with their care. Our parents are now in a SNF together, but we're the ones visiting, handling calls and concerns, taking care of their finances, bills, taxes and buying anything they need, etc. We have an estranged sibling. This one has her own family and we understand she's busy. Early on when our parents started their quick decline, I sent updates to this sibling. She in turn threatened to file a report against our sister because she had heard that she raised her voice at Mom. (This estranged sibling rarely visits and is never involved in decision making so she doesn't know how stressful this all can be!) I don't agree that my sis yelled at our mother, but again... emotions run high for everyone during this time of our life. Mom and my sis have since moved past this. I've tried to include the estranged sibling. Such as when my parents needed to move out of their ASF to a SNF, my parents agreed that estranged sibling should arrange to pick up the furniture they want to keep. Sibling came by, left a single note on what she wanted and that was it. Never came back. Baffled Mom and Dad. Come move out day, all of the furniture was still there. Being on a time crunch, we moved the furniture to storage. It's ridiculous. Anyway, the updates I sent to my estranged sibling are never acknowledged with any concern or discussion so I stopped sending them from my personal number or email. Under my father's advice, I started sending updates through my Dad's email instead. (Of course, this sibling has a problem with Dad too. And never responds.) This sibling has made some questionable decisions in the past that makes everyone wary of her. She's got an unpredictable personality and temper. I know she's busy with her own family but I know she's close to Mom. Mom's health is declining quickly. Other than my sneaky emails with Dad, I don't know how else to reach out. This sibling is always defensive and she believes everyone thinks she's crazy. I decided to not talk to her when I see her in person because she can always mis-interpret your well-wishing or just doesn't trust what you say anyway. I've tried to make amends and every single time it blows up in my face. My partner has long since advised to let it go. It's such a sad mess. I guess writing it out helps give me perspective in knowing that Mom and Dad's care is the top priority. But I can't help that this sibling might be feeling abandoned... but then she doesn't make it easy for anyone to talk to her. (Back when we were on speaking terms, she only ever talked about herself. And it was always to complain or drag up her own grudges that the family has long since moved on from. She would talk about her hateful grudges over and over again at every conversation! In the end, I stopped calling and taking her calls. I told her she needed a therapist.) Anyway, I'm afraid of what will happen when our parents pass on. Answers will only come from communication, but it's like talking to an angry wall and I want to protect myself and my own loved ones.