Thank you for your Question.
وَقَضَى رَبُّكَ أَلَّا تَعْبُدُوا إِلَّا إِيَّاهُ وَبِالْوَالِدَيْنِ إِحْسَانًا إِمَّا يَبْلُغَنَّ عِنْدَكَ الْكِبَرَ أَحَدُهُمَا أَوْ كِلَاهُمَا فَلَا تَقُلْ لَهُمَا أُفٍّ وَلَا تَنْهَرْهُمَا وَقُلْ لَهُمَا قَوْلًا كَرِيمً۳
Allah says in the holy Quran (Israa:23):
And your Lord has decreed that you not worship except Him, and to parents, good treatment. Whether one or both of them reach old age [while] with you, say not to them [so much as], "uff," and do not repel them but speak to them a noble word.
The Ayah is self-explanatory and by the creator Himself.
At 80, some people do have issues with not being able to control the self, whether it’s talking, actions etc.
But children can really help and moderate their shortcoming in the family.
Also, your mother has a point by minding the free entry and exit of male classmates of her grand daughters in the house. In reality, it isn’t her but It is Allah (swt) himself who despises such relations and identifies them as Haram!
In this case, your mother is really a blessing and her presence is at least an hindrance to this act.
This is what I have to comment on case before your Question.
As to your Question, It is ok for a mother to live with her daughter however if this move is enforced on her by her children and she doesn’t like it, and also trails her unhappiness then it should not be done. Also, in your title you mentioned unwilling sister, which would mean that you sister is not happy with her mother being in the house and this could one way or the other have an impact on your mother and her happiness. Hence, the answer would be no different than already mentioned above.
Hope this helps