There isn't really enough info from your posts to say where right or wrong lies - and there doesn't need to be.
Your sister is an adult and you can't and shouldn't "give her a shake". Neutrality is the best you can do, even if you secretly agree a fair bit with your sister.
One thing to remind your mother: NC is not always permanent. Give it some years then it maybe will become easier between them; a bit of distance and breathing space helps a lot, sometimes.
Would it help your mother to remind her of that, and suggest the best thing she can do for now is to give your sister the space she needs? much as she misses her?
In practical terms, about phone calls. Would it be an option to say "i won't be answering the phone now til 18:00, but I'll ring you after dinner?" Giving her a time when you will definitely have contact will maybe help her feel reassured.
Alternatively, get a new phone and give the number just to your mum and answer when you can. Either simply ignore her - completely- on your main phone or, if it becomes unbearable since you're working from home, if you must block her for a couple of weeks. She'll always have your new phone no to contact you on.
Regarding her always bringing it round to your sister, if you are the stage where you find yourself wanting strongly to avoid her then the situation will go downhill. She does need time to grieve, I can't even imagine what it's like to have a daughter still alive but not wanting contact, though the situation occurred between my half-sister and her mother. There was extremely good reason for my half-sister to go NC though.
You've tried changing the subject. If that still doesn't work, perhaps the next step; would it be possible to use a kind of conditioning on her? If she brings up your sister then to outright say "mum can we please talk about something else". If that doesnt work, then "Okay mum, I need to go". To literally leave, if you have to. Ring her after a couple of days to make sure she's alright. If she challenges you, say that you asked her to leave the subject as you really think it needs space and time to heal, and that you think she needs to build up her own hobbies in the meantime. Not saying -never- let her talk about your sister at all, but to shut it down when you are at the totally-fed-up point.
Your mum needs time to grieve, but if you are so fed up that you are becoming alienated yourself then you have to take stronger steps so that you don't end up avoiding her yourself.
I -don't- think you should talk to your sister much about this, or at anything other than the lightest level. You see her once a year and aren't that close. Pushing your sister might well simply push her away from you.