Oh Audrey I feel so for you,to be caught up in this awful unbearable situation and have your hands tied, must be exactly that unbearable.

Don't be put off by the it's none of your business, IMO it is EVERYONE'S business if you know an animal is not being taken care of properly, whether it be a stranger or a family member.

Only you know you sister best, but see if you and your mother can talk her into it,please for the poor dog's sake, this does not sound an ideal home for it, and if you can do something about it that would be great, it sounds like you have been doing heaps already to help the poor dog, educating your sister to the best of your ability even if it is going in one ear and out the other, it is sad to see someone of her age being irresponsible with a pet, she is NOT teaching her children anything good here either, the cycle will probably repeat, hopefully not as both you and your mother are great pet owners and genuine animal lover, I can only hope that you both rub off on her children and eventually her as well, GOOD LUCK you are going to need it, and fingers and paws crossed for a good outcome .