Adjustable Parts require a set of specified variables that are given values when placed in the assembly. How those variables are given the values varies based on what you want but can be any of the following: An assembly variable, a manual measurement, a keyed in value. For your assembly I would recommend placing a PMI dimension to get the diameter of your cylindrical part and then use that as the Variable to pass to your band. It will update as the cylindrical part changes size.
Build the inner parts in an assembly insert a new part edit the part then copy the outer body surfaces into the new part patch one end of the split surfaces, then trim it to the hoop width the convert the surface to sheet metal. every time the inner body is changed the surface will update thus up date the hoop.
Model the barrel as you want it (after all its the “driving” part).
New file and part copy of the barrel as construction body. Surface → extrude → include the outer edge of the barrel → thicken… and add whatever extra you want to add.
This workflow is only valid in ordered mode if you want it to autoadjust.