Thank you all for your thoughts and suggestions. I have been involved, but, I have been walking on egg shells trying not to take sides with either one of them. Just listening and offering suggestions on how they could expand their true knowledge of what is happening and work together for the benefit of their mom.
I also have been thinking about it considerably and feel that we have reached the point where I have to make my feelings known to them in a way that doesn't say to one that she is wrong and the other that she is right. They both have a right to their own feelings on these matters. The problem is that there is a third person that is the recipient of what ever decision they make, which at this point is to do something that will be extreme in a perhaps vain attempt to make her life better or to do nothing and let it reach its own conclusion.
In this case I tend to agree with what Gabe said. It seems like it is an unnecessary procedure that will not ever have a happy ending and all because we (collectively) don't what to see someone we care about pass on. But, as we all know, that day will come to us at some point anyway and how we get there is as important as when we get there. She has already been diagnosed with less then six months left by her doctor otherwise Hospice would not be involved, which they are. They think that it is possible for her to be trained to swallow again by physical therapy and even some tiny electric charges attached to her neck stimulating muscles to act like they should for swallowing. But, part of the problem is that she doesn't have control of her tongue muscle either that prevents her from speaking in a communicable way.
Add onto that the fact that her past mental health issues have made it easy for people to think that even if she communicates that she does or doesn't want something that she may not be able to mentally be able to understand what is being said. She has lost her short term memory but can and does know the girls instantly. I'm not buying that she is not aware of what is going on. The go and visit her and ask if she wants to play Uno. She nods yes and then proceeds to play properly. To me that means she is certainly capable of thinking in the present and knows and can follow directions. She has a Masters Degree in Nursing and although it is possible that she doesn't consciously remember a lot about it, inside she does understand. When asked if she wanted a feeding tube, she replied with no. When asked if she wanted to have therapy for speech she said yes. I am not buying the not mentally able to make a decision crap. I know her fairly well, I know that she herself made the decision to not have her own mother have anymore extreme prevention when her mother was dying of cancer. She made the decision to make sure that her mother was medicated for pain in spite of the fact that she knew that it might really speed up the process of her death. (It did, she passed away that night)
I guess the time has come to try and rescue my children from the burden of the decision and take it on myself. I will do that because I feel that she will be better served by giving a path for them to follow instead of just asking what path the want to follow. There is a definite fork in this particular road. I am going to give some thought to how I want to say it and then, hopefully give them a way out of decision making while still being part of it in a way that they can live with later.