How to handle taking over finances when mother has been scammed out of thousands of dollars through the mail and phone?

It's too bad that one of your siblings is so against this. Of course, your mother is upset. But her history and the agreement of the doctor shows that you are right. You'll have to lovingly detach from her anger. Acknowledge how hard it is to give cup control. Make sure she has some money to spend. But let her know that her doctor thinks this is best. If you can document her history of these scams and show it to the sister who objects, then you can ask her why, exactly, she objects. She may just be softhearted and hates to see her mom upset. But she needs to know that her mom in in a self-destructive mode and that she needs help. Good luck. This is never fun.
Carol