Your sister is 100% responsible for her own actions and behavior.
However, BOTH of your parents are responsible for enabling her behavior. Your mother may have to 'deal' with her the majority of the time, but they both have agreed to repeatedly bail her out financially.
You cannot change your sister but you can establish boundaries of what is acceptable behavior and what the consequences are for poor behavior. You cannot dump this on your mother. It will take a collaborative effort by the entire family. You need to agree on the boundaries and agree on what the responses are when she breaks these boundaries. Most importantly, everyone must stick to them! All it takes is one person giving just one little bit and the whole effort is lost. I suggest you seek the aid of a professional therapist to help you work through this and set those boundaries/responses. Everyone should also be aware that when you implement the new boundaries and consequences, she will dramatically increase the amount and instensity of her bad behavior. It is will become much worse at first, but if you stick through that storm, it will get better.
Best of luck to you.