I completely agree with the recommendation of quincy and others to see a doctor for a balance problem. At whatever age, never just assume it is the consequence of aging. I know someone not yet 60 that is experiencing balance and motor control problems. According to his doctors, there are a lot of different reasons why people have this problem and it's important to get it checked out earlier rather than later no matter how old the person is. Also, the treatment of some conditions is much easier and the results are much better when caught early.
If your mother sues she can't be certain that she won't be compelled to testify by defense, known as a cross-exam. Cross examination can be very difficult either because the witness feels very uncomfortable in that setting and fears saying the wrong thing, or because opposing counsel is one of those types that do rapid fire questions that don't give the witness time to think or the opposing counsel comes across very strong or even intimidating.
For just about anyone, the first time testifying produces at least some anxiety because they don't know what to expect. One way to help that is to have her attorney go with her to one of the open courtrooms and show her what looks and explain what she'll see and hear in that courtroom. Showing her some videos of several different styles of cross examinations would help her see what kind of questioning she may. Those things won't eliminate all the anxiety and fear of the courtroom, especially for older persons who don't adapt well to new things. But it may at least quell the anxiety of having no idea what will happen.
Initial consultations with many malpractice/personal injury lawyers are free or low cost and that would give her a much better sense of how strong her case is and what to expect. She may want to consult several to find one that she's comfortable with. That's what I suggest she does first befor any further metnion of a lawsuit to others, particularly with the defendant or the defendant's representatives.
Unfortunately, with people who are quite elderly jury awards tend to be low because they aren't losing any money from work and much of the medical cost she incurs is probably paid by Medicare/Medicaid. There are some states though that exclude evidence of government assistance to the plaintiff. But even it it's not mentioned, at least some jurors may assume she's getting those benefits and take that into account in deciding what an appropriate award would be.
I wish her the best whatever choice she decides to make.