Is it permissible for me, Islamically speaking, to remain in the house I rent from my sister, knowing there is a legal dispute between us regarding my eviction from it, and that my sister deceived my mother concerning the ownership of another house?

Kinship ties must be maintained, even if they are severed, for Allah connects with those who maintain them and cuts off those who sever them. As for renting, a time period must be specified. If no time period is specified, such as in a month-to-month rental agreement, then it is not binding on either party, and each has the right to terminate the contract unless the rent has been paid, or the month or year has begun.