What is the religious ruling on my refraining from helping my sister after she bought a house in another city at her own desire, and was my mother wrong in preferring and helping her over the rest of her children?

Contributing to help your sister with what you can is a part of maintaining kinship ties, which is commanded by Islamic law. Allah has promised great rewards for it in this world and the hereafter, as the Prophet, peace and blessings be upon him, said: "Whoever wishes that his sustenance be expanded for him and his life span be extended, let him maintain his ties of kinship."