Assuming your contract with the subcontractor does not require the shop to have a PP or S stamp; I believe the answer to your question is contained in ASME Section VIII, U-1(c)(2)(e) - (not included in the scope of the code, therefore, no code authorization is required for the part you describe):
"piping components, such as pipe flanges, bolting, gaskets, valves, expansion joints, fittings , and the pressure containing parts of other components, such as strainers and devices which serve such purposes as mixing, separating, snubbing, distributing, and metering or controlling flow, provided that pressure containing parts of such components are generally recognized as piping components or accessories."
Basically, you have described quite well what your pressure vessel is. Referring to U-1(e)(1)(c), you see that the flanged face of the first flanged joint (on the pressure vessel side) is the boundary.
The spool piece you describe attaches to that joint, and is "generally recognized as a piping component". To repeat myself, no code stamp is required for the manufacture of that part.
Although the spool piece manufacturer does not have to possess an ASME stamp, if they are producing a spool piece for use on a pressure vessel skid for you, you have the right to reject the component if it fails weld quality acceptance criteria established by your contract with them.
Charles
I'll make a comment on your statement that "There is a short piece of pipe etc. The pipe is a 90ยบ elbow with a butt weld flange on each end".
No flexible joint to absorb the compression vibration? Even the centrifugal compressors vibrate, to say nothing of the recips.
Did you never feel the need for a flexible joint ? I'm surprised.
Welds subjected to continuous vibration tend to show cracks in the long run.
Giovanni S. Crisi
Sao Paulo - Brazil