As I've grown older, I've realized that life doesn't get any easier, and often we face choices we wish we didn't have to make. To put it another way, what we once saw happening to older people is now happening to us -- whether we like it or not!
In all honesty, you probably can't convince your mother to move until she either realizes she can no longer take care of herself, or else something happens that makes it necessary for her to move (such as a medical crisis or declining mental ability). It's important, therefore, for you and your sister to keep monitoring her situation, while treating her with respect and patience. From what you say, I suspect that the more insistent you are, the more she'll resist doing what you want her to do.
At the same time, I suggest you explore other options for her care. For example, she might be open to having someone come in during the day to help her. Not only would that enable her to stay in her home, but it might be less expensive.
The most important thing, however, is to assure her of your love, and most of all, of God's love. The older we get, the harder life often becomes. But God hasn't forgotten us -- and ahead of us is heaven if we know Christ. God has promised, "Even to your old age and gray hairs I am he, I am he who will sustain you" (Isaiah 46:4).