How can I call the default inspector (from OnInspectorGUI for example) of a class that I don’t inherit from ? (otherObject.DrawDefaultInspector())
You need to first create an Editor of the appropriate type. This is accomplished with Editor.CreateEditor. The documentation for CreateEditor has an example too, but basically, in your OnInspectorGUI, you do:
Editor otherEditor = Editor.CreateEditor(otherObject);
otherEditor.DrawDefaultInspector();