Hi VD,
Although I am not an expert (in fact I am a propulsion engineer - turbojet, bypass, turbofan, turboshaft engines, namely gas turbines) and I am not quite sure that I understand your problem correctly, I'll try to give some kind of an answer.
My problems are that your 'application' of the terms "composite" and "sandvich" is confusing me and a trade name "nomex", which I do not know of.
Composite material is in fact mimicking of a wood material (that is my interpretation, because composites without reinforcing, "organized" fibres are not composites to me). There is a matrix (carbon, epoxy, or some other resins, even ceramics in hot sections of my beloved engines) and reinforcing fibres (again carbon, "kevlar" which I do not know what actually is, glass or metal).
Sandvich in aeronautics is almost exclusively two sheets (metal or even composite) with honeycomb structure inbetween
(usualy Aluminum, an aircraft cabin floor may be of a such construction - all made of Al). Therefore I will assume that your structure is a sandwich: carbon sheets and that "nomex" inbetween (no composites).
Usual aircraft repair procedure is to manufacture a flanged oversize bushing (from Al or maybe some hard, wear resistant plastic in your case). Then to machine a matching "nest" in that sandwich (make that hole bigger to mach the bushing O/D and a counterbore for the bushing flange if structurally OK, if not flange will rest on the upper sheet). The next step is "bonding of the bushing (to the honeycomb-"nomex" using some of the structural adhesives or already mentioned epoxy and a final machining of the bushing hole to required location and diameter after adhesive curing. Usually bushing is predrilled but not to the final I/D allowing for final hole location correction but if location is not so important (your civil "tolerances" tend to be plus or minus inch, sorry but I couldn't help teasing), than I/D may be mashined to a required dimension while manufacturing the bushing and it could easily be installed in that sandwich with plus or minus 0,020" accuracy, I believe.