My sister is 51 and has been a problem for my parents since she was 14. She went to my mom's because she didn't have a place to live. My mom had a doctor write a note saying she needed around the clock care so she could stay at my mom's place. My mom doesn't remember all the underhanded things she has done in the past. Since she moved in with my mom she has stolen all her jewelry that was worth anything. My mom had to hide her purse so my sister wouldn't steal anything. Now she talked my mom into letting her handle her finances. Mind you a year or so she got my mom's debit card and spent around 200.00. My mom wouldn't do anything. That's the problem my sister would get in trouble and my mom would bail her out. She doesn't treat my mom right unless she wants something.
Collect everything you can to show what your sister is/has done. Take it all to an Elder Law attorney and go for Guardian/Conservator for your Mom. Your sister tries to fight, the evidence will be placed in front of her and she may end up being arrested for Elder Abuse.
Go for it before she leaves Mom in a home without heat/AC, no food, bed bugs. Please, trust me on this.
remove an lock up all the check book, savings passbooks, etc.
change all passwords and contact the credit reporting bureaus and lock her credit so new accounts cannot be opened.
then work out a process with Mom...maybe twice a month you and she sit down and handle all the financial issues. Write checks, authorize direct payments, etc.
But...if Mom is not willing to do any of this, and she is competent... then there is nothing you can do except sit and talk with Mom and try to make her understand that it is her own future she is throwing away. Ask her..does she believe that your younger sister will ever pay her back? Does she believe that when the time comes the money is gone she will go live off your younger sister? Make sure she knows that you will not be the person that provides for her once she has given her money to the younger sister.
that really all you can do.
the biggest issue you face after that is to be very certain you are not the one ending up hurt by the actions of your sister.