Fully define the other component. It should stop it from rotating when you rotate your part.
First of all make your assembly fully defined. All the parts,sub-assemblies etc should be fully defined. Then, whichever part you want to rotate, give only to mates to it. i.e., one is concentric mate and other is surface mate. Then simply left click on on that part and try to drag it, it will rotate. The problem with your assembly right now is you main assembly is not fully defined with mates. So whenever you want to rotate that one part, your entire assembly starts rotating/sliding/change their respective position (because they all are not mated to fully defined).
Attach your assembly here and end all doubt.
Temporarily suppress all mates associated with the other messy components. Rotate part as needed. Unsuppress mates.