First, some GOOD news. That stage 4 thing isn't the death sentence it once was. PLENTY of people are being successfully treated, but see if she can get into a clinical trial of the new drugs, for a little extra edge. As for the rest:
There are, indeed, many "born again" Christians who have recovered and bounced back from some dreadful prior life and experiences. Whether it is the real deal, or just the latest from of denial - only time will tell. But your mother's case appears to be genuine.
And it is not untypical that the newly baked Christians go through a period in which they feel compelled to drag everyone else along on their journey. In many cases, but not all, they eventually become a bit more seasoned, and realize that the positive changes they may help bring about in others will come more as a result of their own example and obvious happiness then it will because of their preachments. For the rest of us, it means some tolerance and patience is required. The nonsense about your son's autism as a form of punishment is a classic case. Sooner or later, they will have an experience, or conclude through thought, they they've gone a bit overboard.
Meanwhile, for yourself, freely leave God out of the argument, and be guided by the moral compass which has thus far served you well. The deal with mom is that, one way or another, she needs treatment, and you need the intestinal fortitude to see this thing through. And as for the psychiatric cases who would have you think you are worse for being faithless, your instincts quite clearly, and quite correctly, tell you otherwise. I'll drag this much of my own religious persuasion into the matter: If Jesus appeared before you right now, he would, just as he once did, castigate those who judge you, reminding them about that casting of the first stone. And he would then turn to you and say, "Forget about believing in me, and for right now just believe that someone needs to get a grip, here, and guess what - that's you!"
You are going to suffer through a lot of nonsense from well meaning, and not so well meaning advisers here on Yahoo who will attempt to convince you about God's plan, your opportunity of salvation and similar themes. Be grateful for those who express sincere interest and as forgiving as you can about those who would put you in their spiritual test tubes. And in all things, keep your focus.
I wish you the best.
EDIT: So good to see your response. I had wondered whether mother might "go it alone" on the remaining cells, and can appreciate your great uncertainty about the outcome.
I was unaware that you are not immediately present, but now do realize you operate "long distance." Owing to this, the only thing you can do, really, is support her as and where she is mentally and otherwise. Forgive me when I say I very much wish I was a nearby personal friend, who could give you a little punch on the arm and help you work though it.
I admire you for maintaining your disposition. Of all the people involved, you most assuredly occupy the high ground, and being true to yourself is exactly what you must continue to do.