I’m glad I came across your post because I have also seen situations similar to yours and I may not know the best course of action, but I can only give my advice.
I can understand how your mother thought that her way of raising her child was to help her get over "the way she is", sometimes people believe that if you are hard on them, that they will change. Today we know the signs of abuse. I have seen people beat children because they are crying. But it doesn’t work that way right. We know that now from many many years of serious scientific studies about human behaviour. Its is now becoming common knowledge. But I’m very sure the way your mother raised your sister has played a big part of the way she had developed. I have seen it before.
But it is true there are studies that say that a high amount of people with ds by the age of 40 will eventually develop Alzheimer's disease. And since it runs in your family it is also very likely.
I also understand how you just need to get away, how hard it is to hear her repeat over and over again, do you have any training in special needs? If not it may be even more difficult for you, sometimes you just don’t know what to do to stop a certain behaviour. and if you were not related to her, I’m sure you would easily quit your job, but you love her so you won’t.
I personally would think of other options before you consider ever sending her away to “special care.” Because its not so special. The years of damage your mother has done without knowing, could take years for her to improve, and I don’t think a care facility can do that, they will only accept the way she is, and give her food and send her to bed. One thing that I found with people with DS similar to this is that they need someone next to them constantly. My advice is that you hire help to come in to your home full time. Or even part time, that extra help with your sister will do you, your husband, and your sister loads of good. She can then have someone with her all the time, weather it’s you, a social worker/special care, or both of you. but you can't be with her all the time without going crazy O_o
But the benefits of hiring help could do her lots of good, and the benefits of her living with you could also do her lots of good. Together, you can really give your sister all the love she needs so she can return that love to you.
Another thing you might want to consider is learning sign language, and while you talk to your sister sign as well. I have read a lot about the benefits of sign language with people with down syndrome, and with children, it is proven that the brain is a muscle and it needs to be worked all the time. Speaking language might be harder for her then most. Maybe she can hear you, but she just cannot respond. and so she just keeps repeating nonsence... We all work with different parts of our brain, everyone (including myself) are stronger in some areas and really struggle in others, all of our brains have developed differently.
Many older people work their brain everyday to prevent Alzheimer's disease. And I have heard of studies that have shown great results with studding and working that muscle. the brain is a muscle and if you work it it will get stronger. In a sense learning sign language might be something to benefit your sister. And if you do decide to try that, it is great to also teach your children. And see if the help you hire would also be interested it trying that.
I'm jsut giving some options to try and make things not only better for your sister, but also better for you. I really sympathize with how hard this is for you.