What is the best exercise to strengthen the muscles around a previously dislocated shoulder?

It depends....: There are many exercises that can strengthening the muscles of the shoulder after a dislocation. However, these exercises may depend on the type of dislocation (anterior vs. Posterior), as well as if there were any other injuries (nerve entrapment, tears, etc.) best to consult with your family or sports medicine doctor, orthopedic surgeon, or physical therapist for specific recommendations.

Anterior Dislocation: Most dislocations occur when the humerus shifts anteriorly in relationship to the glenoid = anterior dislocation. I suggest a thrower's 10 program (http://www.Orthonc.Com/sites/default/files/forms/physical_therapy/sports_protocols/throwers_ten_exercise_program.Pdf) with bands/ light wt. Avoid tricep dips, & push-ups/ bench (w/ >90 elbow flexion) b/c these position the shoulder in a vulnerable way.