Extended service contract have a specific procedure for diagnosing, then repairing/replacing anything. Diagnostics are not normally a covered expense. After the shop diagnoses the problem and contacts the ESC, ONLY THEN will a covered expense be paid by the ESC. If the shop just throws parts at the problem, you then have grounds to protest any charge for unneeded parts, based on the shops diagnostic charges YOU paid.
I don't know about your MH, but mine has a separate "V" belt driving the compressor pump, that belt was loose causing a squeal when the compressor kicked-in.