My mother is having sudden left-sided muscle weakness with double vision and tingling in her arm and leg? What could this possibly be?

Call MD asap. People with sudden onset of weakness and numbness on one side of the body raise a strong concern for possible stroke, particularly when associated with possible brainstem signs of double vision. Early evaluation and/or treatment is very important to prevent worsening of deficits and/or possible treatment.
Take her. To the emergency department preferably by ambulance now! she needs to be immediately evaluated for a stroke...