Sorry to hear about your family situation. Having a sick parent is very stressful, especially for children who rely on adults to provide safety and security. Being stressed out affect all facets of life, even concentration. Your sister might worry about her mom and her illness. She might even be depressed. I would suggest that your sister sees a counselor ASAP.
Im not an expert but I was 15 when my Mom passed away from pancreatic and ovarian cancer. In my opinion I feel that your 11 year old sister needs to be there with her mom during Chemo no matter how much her mom doesn't want her to see her like that. I went one time to my moms chemotherapy and my mom didn't want me to go anymore b/c it made her feel upset that i had to see her like that. Your sister also needs to spend as much positive time as possible with her mom that way in event that her mom does pass away God forbid that she will have more closure than she would have now. She needs to be with her mom. If they have a bad relationship encourage her to make it better that way she won't regret not making it better in the first place. If she doesn't make it better then she will constantly self distruct in later years. Also I also reccommend some counseling. She needs someone to listen and offer her advice that is professionally capable of doing so. I hope your mom gets better!!! Have faith!!! God bless!!!
I'm assuming she knows what's going on with her mom. Maybe try talking to her and see if you can get her mind off of it for a while. Showing her that she doesn't have to stress over something that she has no control over. Keeping her occupied mentally and physically may help. Hope that helps.