What should a caregiving child do to protect their parent from an alcoholic child who using emotional blackmail to bypass family wishes?

Can you provide more (nonidentifying) details?

What are family wishes? Is mom competent? What are mom's health issues? If mom is competent she has the legal right to make her own decisions. It is very hard to watch, but not much family can do.

How is he bypassing the caregiver? Does the caregiver live with your mom? Is your brother blocking the family from coming into the house or seeing/talking to your mom? What wishes is he bypassing? Does your mom agree that he's an alcoholic? Can you have an intervention for your brother and get him into treatment? Call 911 when he gets into the car and you suspect he's been drinking? If you can remove him from the house for 30 days your mom (with family support) can go through an eviction process so that he has no legal right to move back in. Change the locks and during that time have some clarifying but gentle discussions with your mom and make sure a reliable, local family member has her durable Power of Attorney.