64 y.o. with difficulty walking

My mother is 64, in good health, not overweight, still active.  She doesn’t exercise regularly.  Mentally, she has difficulty with things like remembering appointments.

She has issues with her lower body.  She has a shuffling gait, difficulty lifting her feet very high when walking.  When she takes a step, her torso moves forward before her lower body.  She trips a lot.  It takes her a moment to get her feet moving.  She has always had narrow hips, but it looks like her knees are coming closer.  When she turns, her upper body turns first then her hips and legs follow - a twisting motion.  She often falls forward and has to catch herself when turning.  While sitting, her legs shake.

I’ve reenacted her walk, letting my torso move before my legs, and its easy to see why she trips, why she falls.

She’s told me she has to "tell" her legs to move before they will.  Her upper body is still fairly strong, though her shoulders are beginning to sag and her hands have lost some strength for normal tasks - popping the lid off a Tylenol container, for instance. Her...response time seems to be slowing as well.    

Over the course of a year, I can see that these symptoms have worsened.  This does not have the air of normal aging.  I envision her in a wheel chair in the next 2 years if something isn't corrected.

She saw a chiropractor recently who did a few tests, like touch your finger to your nose, which she had difficulty doing.  He suggested she might have a brain lesion from an old accident.  Scared her, needless to say.

She’s has an appointment to have her legs measured to see if one is longer than the other.  Other than that, what suggestions can you make to discover what this is?  Does it seem purely musculoskeletal, or does it seem neurological?  

Exercise should help, shouldn't it?  Additionally, what are good preventive steps she could be doing?

Thanks in advance for your thoughtful input.

Boulder, CO