Because she does not have capacity to sign a power of attorney, you will need to petition to be appointed her Guardian.
Disclaimer: This answer does not create an attorney-client relationship. You must not rely on it for legal advice. The answer might be different if more facts and details were known. Procedures and standards vary for each individual case.
I’m sorry for your loss; you must have a lot on your plate right now. Based on your description of the situation, it seems that you were named a trustee over certain property left in trust for your sister’s maintenance. This is different from the powers needed to manage her personal affairs, and would only give you authority over the assets in the trust. What you would need in order to manage your sister’s health and financial affairs is a power of attorney. Typically, the easiest way to get a power of attorney is to have the subject of the power sign the necessary documents with an attorney present. They can only do this if they understand what they are signing and why, which appears to not be an option for you. In that case, you must have your sister’s handicap documented by a physician or psychiatrist. It is usually best to get a second opinion. These doctors’ reports must demonstrate that your sister’s handicap is severely affecting her ability to manage her physical and financial well being. You will then have to take the case to state court to be evaluated by a judge. If the judge decides that your sister is indeed incapable of maintaining her own interests they may then grant you the power of attorney. I would suggest you contact an estate planning attorney in your area for help representing you in court. Best of luck.