Disclaimer: I am not licensed in NJ. Please note that this answer does not constitute legal advice and should not be relied on because each state has different laws, each situation is fact specific, and it is impossible to evaluate any legal problem without a comprehensive review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
You need to consult with a qualified Elder Law attorney. NJ law may provide that your sister's living with your mother in mom's house for 2 years prior to going into a nursing home for the purpose of providing care will be enough to preclude a post-death estate recovery lien. Only a qualified NJ attorney can tell you if your family has done enough to ward off a lien.