I have been in your shoes. It isn't easy. I lived with my parents while my husband was in grad school. My oldest has Aspergers and all 3 of my kids have sensory issues. Your daughter sounds like she has very strong sensory issues along with other issues with the autism.
I would tell your dad that the kids cannot share a drink after daughter has started one because it is germy. They cannot share a toothbrush, can they? The doctor would not allow it and it is cold and flu season. There is ALWAYS some bug going around, so this is always an excuse. Have the kids split the drinks before they start to drink them by pouring them into separate cups if this is a big issue.
I think he is just trying to control a life that seems out of control to him. He may be on the autistic spectrum himself. I remember going through a checklist about Aspergers (a type of high functioning autism) with my mom. We both were commenting that my father fit the list far more closely than my son did, and my son fit it very closely. I bet no one would have thought to diagnose your dad any more than anyone thought to diagnose my dad.
Whatever is going on, the important thing is to find a way to stop having your daughter get triggered. Is the house large enough to keep them apart more? Maybe have your daughter play in a different part of the house rather than near him?
I also know it will be hard, but you need to stick up for your child. Point out that your child has a DISABILITY that is not her fault. Tell him flat out that he needs to be understanding to her and to not try to be mean just to set her off. IF there is a problem with something, ask him to come to you rather than to insist that your children drink from the same container. Not only is that unsanitary, it is something that will put a great deal of stress on a child who cannot cope with it. doesn't he want her to enjoy spending time with her grandpa?
I would play up that guilt if it were my dad. Of course that worked with my dad. I used that quite a bit with my kids because my dad had a lot of trouble understanding the problems and thought we should just make all the kids do what my oldest wanted. That didn't work for the other 2, and why should they have to have their needs ignored? Having a daughter who was the most adorable creature on earth as a little girl helped a lot. Especially since she could cry on cue. It worked very well with my dad every time. He would think of how cute she was, and then he would actually see her. If he asked her about the subject she would get that chin quiver and a few tears in her eyes, with maybe one or two threatening to spill over but being bravely held back. She was GOOD at that nonsense and it took him years to figure it out. Which I found hilarious. Mostly.
I STRONGLY suggest that you get your daughter into an Occupational Therapist for testing for sensory integration disorder. Most people with autism have some degree of this. Sensory Integration Disorder is when your brain doesn't process input from your senses in the way a normal person's brain does. The world is always "too". It is too much or too little. You either need more of a sensation or type of stimulation or you need much less. It can be a type of motion, a sense of pressure on a part of your body, a sound, a taste, a smell, literally anything that one of your senses can detect. You either have a hard time detecting the world around you, or you feel you are being attacked by it.
How do I know how it feels? I have it. It doesn't go away as you get older. It just becomes something you learn to live with even though it makes you very strange. I am the pickiest eater in my house, mostly because many food textures are just wrong for me. Or else the flavors make me gag. Textures are a big problem for me. Fabrics, cotton balls, styrofoam, many other things are difficult for me to handle. I had to figure out ways to work around them or to do without them. I also cannot be around scented products for the most part.
What do you do for someone with Sensory Integration Disorder? Especially if you start young, you can do a LOT. The Occupational Therapist will evaluate your daughter and then will probably suggest brushing therapy. This is something you can do at home, but you MUST be taught by an Occupational Therapist (OT). You use a soft surgical scrub brush in a certain pattern over the body and then you follow it with gentle joint compression. This actually will retrain the brain to handle input from the senses in a more appropriate way. As long as you do it the way you are shown, there are no side effects and most children either enjoy it or don't mind it. It doesn't take long either. Just 2-3 minutes a few times a day and you actually create new pathways in the brain so that it handles sensory input in a better way!! With no medication and no scary side effects!
The other part of treating this problem is called providing a sensory diet and sensory breaks. Sensory breaks are short periods throughout the day where your daughter can do sensory activities to help her calm down and sort of center herself. Often these are part of a school day and are written into an IEP. While they take time away from "time on task" doing subject work, they increase productive time because your daughter is more able to concentrate and learn between these breaks.
The sensory diet is much like a nutritional diet. It is simply providing varied sensory input each day for her. I always thought of this as the best therapy from a parenting point of view. So often I had to fight with my son to get him to appointments or various therapies or to do exercises or whatever. This therapy was different. You can probably pick out many sensory activities your child would benefit from because they are activities your child likes. Activities needed in a sensory diet are always things the child likes to do, so the parent gets to tell the child they have to go play with a toy or craft they like to play with for half an hour. That is a gift when it comes to therapy!!!
You can learn more about Sensory Integration Disorder by reading The Out of Sync Child by Kranowitz. You can find sensory activities in The Out of Sync Child Has Fun by Kranowitz. Both are available in libraries. The "Has Fun" book truly is fun. We wore out several copies just by using them so often. Every kid in our neighborhood would show up every time I got the book out, or so it seemed. That was how much fun we had with it.
I hope this helps. I am sorry you are dealing with all of this. I also hope you can get your own place very soon.