Long post: Need advice on helping my sister mend her broken relationship with our mother - assalamu alaikum

Assalamu alaikum. I’m looking for guidance on how to encourage my younger sister to repair her relationship with our mother. I’ll try to be brief but honest. Our mother wasn’t perfect as a parent, but she did what she could given her upbringing and the culture she came from. For background: she grew up in a rural village in the Middle East, entered an arranged marriage as a teenager, was sent to a Western country she didn’t know with no family and no language skills, and had to raise many children with little support. She faced trauma - her in-laws often blamed her when things went wrong, and my father had issues like infidelity and violence at times. That history doesn’t excuse everything, but it helps explain her limits and the ways she coped. My sister is Western-born, university-educated, devout, wears hijab, prays, and reads Quran. Despite that, she doesn’t accept our mother’s past as an explanation for how she treated people sometimes. Our mother was never physically abusive; the worst was harsh words, shaming, guilt-tripping, and misunderstandings in arguments. Even so, our mother has usually been willing to calm down and talk things through afterwards. My sister has a pattern of cutting ties with relatives over disputes, and now she has completely stopped speaking to our mother for over a year. When we lived together earlier this year, my sister would walk past our mother as if she wasn’t there. Our mother didn’t want to force contact; she just wanted to know her child was safe and cared for. Ironically, my sister once left home suddenly for a friend’s place and disappeared for two months, returning after another fallout with that friend. More recently our mother moved in with our brother and his kids. My sister still refuses to visit or try to reconcile, and believes our mother should be the one coming to her to ask for forgiveness. When I remind her about the importance of keeping ties of kinship (cutting off relatives is strongly warned against in the Sunnah and Quran), my sister insists that those warnings apply to in-laws rather than blood relatives, and she’s convinced her stance is supported by religious texts. I’m at a loss for how to reach her in a way that’s gentle and rooted in Islam. Does anyone know specific Quranic verses, hadiths, lectures, books, or personal anecdotes that might help my sister see the value of approaching our mother with patience, humility, and mercy? I’m hoping for resources or phrasing I could use that don’t sound judgmental but point to the Prophet’s emphasis on honoring parents and maintaining family ties. JazakAllahu khayr for any help or suggestions.