Dog in bad situation. What to do?

I have a dilemma. My alcoholic grandmother who has bad dementia that comes and goes has a very small dog we’ll call “Fido”. She often forgets that she even has the dog and lives in the country where coyotes and big dogs roam freely. She often leaves Fido outside without water or food. While granted she acts like she loves her dog when anyone is visiting her, the truth is she hits and kicks the dog to discipline it. It only weighs 5 pounds full grown. I have a farm adjoining her property and see the little dog’s suffering everyday when I am at the farm to check on my animals. While I give water and food, I have several times found it in distress from lack of water and overheated. Over the years, she has had many animals and they all end up being killed by predators or just run away in search of food. So it is just a matter of time before this happens to “Fido”. I recently spent money to have this dog fixed and vaccinated for her at my own expense $$$$ -hoping it would improve its quality of life. However, now after witnessing her kicking at Fido and seeing that she is leaving it out in 100 + temps, I feel that perhaps I need to take the dog and just let her believe it ran away. After a few days (if not sooner) she will forget she ever had a dog. Trying to reason with her is impossible, she has a very violent tendency in her and I truly believe she doesn’t have the skills to care for herself let alone a defenseless animal. While the family members are aware of her situation with dementia and are keeping an eye on her, they are not animal lovers and will not see the reasoning behind taking the little dog from her. They will not think taking the dog from her is right. I am heart sick about this little dog. What do you think I should do? Should I take the dog and care for it without telling any of them , (they never visit me) or should I just turn a blind eye and continue to be heartsick for this dog and let her keep it without interference???