Either your parents own the home or the trust does. If the trust owns the home then the trustee of the trust manages the property for the benefit of the beneficiaries. The trustee can evict people. Sounds more like low level blackmail but she can evict you if the arrangement you have to stay on the property is not in writing in the trust document (or in a rental agreement, etc).
If your mother is on the road to recovery and has her mental faculties, she can possibly amend the trust to make it clear you are allowed to live there without rent; or she could remove your sister as trustee and replace her; in any case you should have your mother make it clear that you are allowed to remain in the residence so long as you desire. From a practical standpoint if you are living there rent free it would be nice if you were to assist with your mother's care, whether your sister demands it or not - she is your mother and we all should care for the elderly, especially our family.
Best of luck.
Mr. Post is licensed to practice law in KS and MO. The response herein is not legal advice and does not create an attorney/ client relationship. The response is in the form of legal education and is intended to provide general information about the matter within the question. Oftentimes the question does not include significant and important facts and timelines that if known could significantly change the reply unsuitable. Mr. Post strongly advises the questioner to confer with an attorney in their state in order to ensure proper advice is received.