There really isn’t such a thing as being double-jointed. Usually this term is used to describe a joint (or a person) that is very, very flexible. In fact, they are beyond just flexible — their joint(s) are hypermobile. In other words, they stretch much farther than is normal.
You’ve probably seen people who can bend their thumb back so far, it touches their wrist. Or people who can put their legs around the back of the head. Any of these contortionists have loose ligaments and joints that allow greater motion than even the most normal, flexible person.
But there is a difference between joint laxity (looseness) and joint instability. Without some special tests, it’s impossible to tell which category your son falls into. Being able to pop the shoulder out of the joint isn’t the type of parlor trick you want to encourage.
This is especially true in a young child who is still developing and could potentially grow out of it. But stretching the soft tissues around the joint each time it’s dislocated will only continue to contribute to the problem. You only mentioned that he does this on one side. Perhaps there has been some injury or damage to the soft tissue structures that you don’t know about.
It’s a very good idea to have an orthopedic specialist take a look at him and give you some idea of what might be allowing him to voluntarily dislocate his shoulder. He or she will be able to offer you some guidelines based on the final diagnosis.