My friend's father had all of those same symptoms, minus the numbness and tingling. MRI revealed rotator cuff tears and mild shoulder impingement. He's 73 and surgery is not advisable.
Cortisone injection, NSAIDS, physical therapy (focusing on scapular strengthening) and rest were prescribed. Also, ordered to "stop injuring himself". He falls occasionally and stops himself with his arms, and that worsens the condition.
Took one year to heal with this treatment.
In most cases, pain radiating down the arm originates in the shoulder, and is called "referred" pain from a shoulder injury.
If your mother has poor posture (rounded upper back, shoulders "flopped" forward) this contributes to shoulder problems.
As for the numbness - I've heard about impingement conditions compressing a nerve and causing such sensations.