p0420 code ? parameters of readings
If you scantool allows, read the Mode $6 data and look at test Test ID 0C:60, it will show you that the subtest has failed...
When the drive cycle conditions are met (freeway cruising followed by coastdown followed by idle), the PCM will briefly manipulate the AFR and time the response from front O2 sensor to rear O2 sensor... if the response time is too short it will fail the cat (TID 0C:60 fails which causes P0420).
A bad O2 sensor may actually make the cat test pass.
An airleak may help it fail easier, maybe.
The shudder/roughness is not related unless the cat is falling apart and clogging the exit pipe restricting exhaust flow.






