Autistic child has pathological liar for mother

I have taken in my granddaughter and her autistic 5 year old. She obviously was in way over her head, unable to cope or deal with her child. Long story short, I have discovered that she is a pathological liar. She is a binge eater, lies about her jobs and relationships with others, which change often, lies about her health, etc. That is troubling enough, but she doesn't seem capable of taking proper care of her autistic child. The child was 4 when they moved in, still in diapers, having meltdowns whenever hungry, thirsty, tired; violent and spent a lot of time closed up in the bedroom. I've witnessed her offering donuts for breakfast, doritos for lunch and pretzels for dinner. Over the past year I have been working with both of them. The autistic child is a delight! Mom seems to be improving, but I don't see her trying to help the child, just be the disciplinarian, my word is my command and will be done instantly this second, kind of attitude. Hates going to any function the child might enjoy and tells me the child is not allowed to go. I later find out differently. When she is home, the child is crying. When she is not home, the child is talkative, helpful, a pure joy to be around. The mother has yelled at me for being too nice when she should be punished for her bad behavior. (The child yells no and has meltdowns because mom commands something be done right now or go to bed.) She is the mom and her word goes!

I don't know what to do. I love my granddaughter but I fear for the child. Please help