Welcome to the board!
You and your sister really have a dilemma. I am sorry that you are facing this situation.
It sounds like your dad is not capable of caring for your mother and not even capable of caring for himself if he is going to drive drunk. Is it possible that your dad would consider going to AA? You could confiscate the keys to the car, but it could result in battle!
If you are prepared to do it, you would probably need to make a call your county's social services and let them know what is going on in the house. They would come to the house themselves to see what the situation is and determine what needs to be done to protect your mom and help your dad. They could tell you the best way to proceed legally. (I am only assuming that your dad is your mom's legal guardian since she is not capable of making decisions for herself.) Of course, then you and your sister will have to face some serious decisions on what to do for your mom and who will take care of her. Your mom is fortunate that she has you and your sister to look out for her welfare!
As for your dad's drunk driving issue, I would pay a visit to the local police department and let them know what is going on. I don't know that they can remove your dad's driver's license unless they actually stop him while he is drunk. Also, make sure you have a record of your dad's blood alcohol level to show them.
Have you and your sister talked about this issue at length and are your both prepared for the backlash from your dad? These are extreme measures to take, so please make sure that your both are on the same...exact page.
Contacting an Elder Care attorney might also be advisable!
My mother was an alcoholic/prescription drug addict and also mentally ill, so I really do understand and feel your pain! Good luck in whatever you decide to do!