Someone who experiences stiffness that gets better with movement is probably experiencing some muscle involvement. On the other hand, people who feel good when first waking up but then stiffen up as the day goes by are more likely to be dealing with issues involving the joints.
Muscle weakness can sometimes be a greater problem than even pain — especially in older adults who have become more sedentary and deconditioned. The first thing is to have a medical evaluation. If she has stiffness everywhere, there may be a systemic reason for that. If she has osteoarthritis, there are medications and exercises that can help.
In fact, many studies have shown that even simple knee flexion and extension exercises do help with knee osteoarthritis. They improve strength and help the knee respond quickly to any change in position. The result can be less stiffness, faster walking speed, and a lower risk for falling.
When it comes to exercise, in any community, there are usually several choices for seniors. Local and public TV stations broadcast programs like Sit To Be Fit or Yoga for Seniors. Fitness centers, senior centers, the YMCA/YWCA, and other similar places often offer a wide range of exercise classes that might be suitable.
It may help to have a physical therapist evaluate your mother for specific areas of weakness for some spot strengthening. The therapist can set her up on a home program and offer rechecks weekly/monthly to make sure she stays on track and progresses her exercises appropriately. Even simple resistance and balance training at home can be very effective for a wide variety of benefits including reducing pain and stiffness while increasing strength and function.