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

Take her: To the emergency department preferably by ambulance now! she needs to be immediately evaluated for a stroke...

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.