The moon at whatever position it is in, has no bearing with regard to joint pains.
People that suffer from any form of arthritis can experience more pain when the weather changes - like when it is going to rain or get cold.
Because your mother wore a covering over her not well knee it is likely that the heat made it feel a little better.
If this is a new problem that has not be examined by her doctor, it would be a good idea to make an appointment to see the doctor and to get an xray done of the knee to see if there is any arthritic changes in the bones that is the cause of the problem.
Some people find rubbing in an anti-inflammatory gel into the knee joint helpful. As the knee cap is helping that is fine, but it is still important to exercise the knee joint so that it does not stiffen up. Good forms of exercise to strengthen the supporting muscles around the knee joints is by going to the local swimming pool and doing walking exercises in the water.
I'm sorry to hear of your mother's problems and pain. Did she injure herself or do anything unusual prior to her getting the pain that she can recall?
Has this ever happened to her before? Does this pain feel like pain she has in her other knee?
Where exactly is the pain (over the knee cap, to the side of the knee, behind the knee, just below the knee cap, etc.)?
Is there swelling, redness, bruising, or warmth to the area?
What makes the pain better? What makes it worse?
What has she tried to make the pain better? Ice or heat, rest, elevation, compression/ace wrap, medications, call her doctor?
Does she take any medication for her Osteoporosis or any Rheumatoid problems? Has her LEFT knee been fine (not favoring it)?
I don't think the full moon would affect her. When you say "knee cap," are you referring to a knee immobilizer or a knee strap or a protective gear that workers use to protect their knees when kneeling?