Thank you for sharing this in depth meditation on your experiences in an immigrant family and the complexities so juggling a cultural heritage while being the 'parentified child'. I came across this expression recently adn I think it's helpful as a lens through which to understand the sense of duty you have adn the resentments of siblings influenced by the Western notion of individual rights... your sister's conduct reminds me of my siblings, entitled behaviour ie they are happy to take according to the heritage values, but cforget those w=values hen it suites their convenience.
Glad you have formed your now family and can heal from this rupture that your mother too, refuses to help overcome.
I am in a similar situation, but with five such siblings !