In the opinion of this Courtenay chiropractor, problems with internal rotation of the shoulder are often a major component of the rotator cuff issues seen in my office.
In office, I will employ soft tissue therapy, chiropractic adjustments and taping to help restore proper function to the rotator cuff and surrounding structures. I also believe it is important to arm the patient with exercises to do at home. One of the most important stretches out there is the Sleeper Stretch.
A great explanation of the sleeper stretch can be found here, with pictures to clarify.
If you have pain putting on your coat, or unhooking a bra, then you may have problems with internal rotation and impingement in the back of your shoulder. See a professional for a correct diagnosis, and ask them about the Sleeper stretch. It can be used to help alleviate the problem, and as a precaution to prevent it from returning.