I made a video on how to do Arm Circles in Opposite Directions. This is something you could throw into your daily warm-up because it feels GREAT and also improves coordination since both sides of your body and brain have to work together.
You could do it as a warm up or whenever you want to just loosen up a little! At first, it may be confusing but with daily practice you’ll be boss at it! Besides, what’s the fun of doing something new if it isn’t at least a bit challenging?
After you practice that and get comfortable with it (it might take a few days), rather than simply throwing your arms around, you could refine the circles further by adding rotations to the circles by practicing Andreo Spina’s Shoulder Rotations:
These rotations are an excellent exercise to maintain shoulder joint health and mobility. I do them daily upon waking. Then, if you want an extra challenge for your mind/body, you could combine the two concepts into doing them with both arms at the same time in opposite directions.
Fun nerdy info: Externally rotating the shoulder as it comes overhead (palm up) and internally rotating it as it goes behind clears the greater tubercle of the humerus from hitting the structures under the acromion thus avoiding potential aggravation of the structures due to impingement.