Volkemon,
He also said voltage at "another" RV outlet dropped below 100."
I presumed he meant another outlet IN the RV rather than the pedestal.
Which is why I suggested he measure the voltage at the pedestal and all the way back to see where the drop occurred.
You lost me there cuz.
I agree, the OP said "First noticed it when A/C turns on then stumbles. Voltage at another RV outlet dropped well below 100."
I took that to mean that the first indicator of trouble was the operation of the A/C, and a voltage drop was measured at an outlet in the RV, and found to be below 100V. I can see where one could interpret that as 'an outlet in another RV' though!!

next line of " Problem persists when disconnected from shore power and generator running." would have me thinking its a problem independent of the shore power pedestal, and points before it in the delivery of power. (Or 'all the way back' as you state - is that what 'all the way back' means?)
But with the kiln comment I was referring to your statement:
" And now you are saying the kiln IN YOUR SHOP causes it?
You are on your own bud."
I misunderstood apparently. I thought your deliberate use of capital letters saying 'IN YOUR SHOP' meant that you thought that the kiln was plugged in inside their shop. Not from the shop, and plugged into the RV as a high current draw test. My bad.

But really... we are talking about a pretty simple electrical system. A voltmeter and suitable tools for access to testing points should have the problem isolated in little more time than it takes to get things apart to measure voltage.
Thru Traffic -
We are dealing with a 30A service. One A/C unit on the coach, and that unit was operating.
The operation of this A/C was a primary indicator alerting you to the problem. Primarily by a 'stumble' after starting, but once it has tripped the 20A breaker.
A/C is now turned off.
Testing voltage at an outlet in the RV, while using appliances installed in the RV
OR other appliances plugged into the RV as a
current draw test, you found less than 100V.
With no appliances drawing power, the voltage measured at the outlet is very close to measured pedestal voltage.
Am I right so far?
If not, please correct me.
If so....
BEGIN DIAGNOSTICS!!! 
TEST CONDITION: Shore power unplugged, generator supplying electricity. Transfer switch has closed, powering coach area from generator. Voltage initially being measured at an outlet in the RV.
Repeat the current draw test, and measure voltage at the outlet that was low before.
Does the outlet reads low voltage?
If no, proceed to "
SHORE POWER ON" below.
If yes, continue.
There is a circuit breaker that supplies the outlet you are measuring with electricity via a screw terminal, with a wire attached. Locate this breaker. Does the low voltage reading appear at this screw terminal also when you repeat the current draw test?
If no, there is a problem between the breaker terminal and outlet. Find and repair. Repeat current draw test to verify repair.
If yes, we must go closer to the source. Remove the cover on the breaker box, and measure the voltage on the bus that the breaker gets its power from. Repeat the current draw test.
Does the voltage on the bus drop?
If no, there is an internal fault in the breaker. Replace with a known good one. Repeat current draw test to verify repair.
If yes, we still must keep 'going back' towards the source.
The transfer switch feeds the power to the bus in the breaker box. Repeat current draw test, and see if the voltage drop is observed at the output side of the transfer switch.
If no, its a fault between the transfer switch and the breaker box. Find and repair. Repeat current draw test to verify repair.
If yes, then repeat the current draw test while measuring the voltage on the generator supply side of the transfer switch.
Does the voltage drop again?
If no, the fault lies in the transfer switch. It is getting good power, and not passing it through. Replace with a known good one, and repeat current draw test to verify repair.
If yes, repeat the current draw test while measuring the voltage coming from the generator. If there are any intermediate junction boxes between the generator and the transfer switch, be sure to test them independently.
Is there a drop in voltage still observed?
If yes, that would indicate an internal generator fault. Find and repair. Repeat current draw test to verify repair.
If no, there is a fault in the connections between the generator and transfer switch. Find and repair. Repeat current draw test to verify repair.
Continue on to the next section.
SHORE POWER ONTEST CONDITIONS: Generator off, Shore power on and supplying coach with power. Voltage being measured at an outlet in the RV.
Repeat the current draw test, and measure voltage at the outlet that was low before.
Does the outlet reads low voltage?
If no, you have no problems indicated. It works fine on Generator or shore power.
If yes, continue.
There is a circuit breaker that supplies the outlet you are measuring with electricity via a screw terminal, with a wire attached. Locate this breaker. Does the voltage drop appear at this screw terminal also when you repeat the current draw test?
If no, there is a problem between the breaker terminal and outlet. Find and repair. Repeat current draw test to verify repair.
If yes, we must go closer to the source. Remove the cover on the breaker box, and measure the voltage on the bus that the breaker gets its power from. Repeat the current draw test.
Does the voltage on the bus drop?
If no, there is an internal fault in the breaker. Replace with a known good one. Repeat current draw test to verify repair.
If yes, we still must keep 'going back' towards the source.
The transfer switch feeds the power to the bus in the breaker box. Repeat current draw test, and see if the voltage drop is observed at the output side of the transfer switch.
If no, its a fault between the transfer switch and the breaker box. Find and repair. Repeat current draw test to verify repair.
If yes, then repeat the current draw test while measuring the voltage on the shore power supply side of the transfer switch.
Does the voltage drop again?
If no, the fault lies in the transfer switch. It is getting good power, and not passing it through. Replace with a known good one, and repeat current draw test to verify repair.
If yes, repeat the current draw test while measuring the voltage coming from the backside of the bulkhead shore power connector. If there are any intermediate junction boxes between the shore power bulkhead connector and the transfer switch, be sure to test them independently.
Is there a drop in voltage still observed?
If no, there is a fault in the connections between the shore power bulkhead connector and transfer switch. Find and repair. Repeat current draw test to verify repair.
If yes, you must test the connection between the shore power cord and the bulkhead connector. This can be difficult, if not impossible to do without a special testing adapter.
If you are this point, and HAVE A KNOWN GOOD SHORE POWER CORD AND PEDESTAL VOLTAGE, I would feel safe in replacing the shore power bulkhead connector. After doing all the testing above you know that all systems on board are working correctly. As always, Repeat current draw test to verify repair.
There. 'Thats all' you have to do for an orderly diagnostic procedure regarding this complaint. Many simple steps, with yes/no outcomes. NO guessing.
Or you can just start throwing parts at it. Many people use that method.

This would be easier to read in flow chart format, but text is what I have available to me at this time. Sorry for the difficulty it may cause.
LOL.. next up: the presence of the slide as a contributing factor to many, if not all RV issues.