I'm so sorry to hear about your mother,I know what you're going through, I lost my mom to complications from diabetes 9 yrs. ago at theyoung age of 46.
As far as the other daughter,is it a half sister,full sister,I definately take it that you two don't see eye to eye on things. I do have a good friend that had the same problem when her mom was dying of brain cancer,her and her sister-in-law didn't get along (The sis-in-law was very mean to the mom)however I have to give my friend alot of credit because she just kept to herself and didn't say anything,just to keep the peace,because she knew that her mom could still hear everything that was going on.She also knew that her mom wanted her passing to be peaceful,and nobody fighting and arguing,and she respected her mothers final wishes.Now I can honestly say that they no longer speak at all,which is fine now and I can understand why my friend was so angry.There was one person that showed up at my moms funeral that I felt shouldn't have been there,she was always mean to my mom,and talked bad about her to other people.But I kept my mouth shut and kept the peace,for my mom. I think that you should try as much as possible to keep the peace for the sake of your mother.If you want to talk feel free to PM me if you want to talk.