A few questions:
The AC doesn't shut off?
*How do you know it didn't turn off? (monitor Amps etc)
What anode rod -----Atwood has never used one. They use aluminum tanks that do not require an anode rod
Atwood uses a 1/2" Nylon Plug (not that anode rod with pet cock)
*Suburban does due to the Steel glass-lined tank
Unable to turn off
Could be the control switch
Both t-stats would have to FAIL closed to overheat on your standard model
T-stat Opens at 140*F/ECO (Hi Temp) trips at 180*F and locks out all heating
**On Gas the ECO triggers Fault Light
**On AC the ECO has to be Manually Reset (hole in cover on backside of tank)
T&P Relief valve can 'weep' due to:
*Loss of air pocket in top of tank
*Old and/or build up on valve seat/disc
*Temp reaching 210*F or pressure reaching 150 PSI
Loss of Air Pocket:
2001 Vintage........Relief Valve is 23+ yrs old
Replace it
Could be 1/2" NPT Relief Valve OR 3/4" NPT Relief Valve
*Atwood used both sizes (remove yours/take with to Hardware Store/Big Box Store----4" temp probe)
PDX is good place to shop/compare parts
Except for the T&P Relief Valve----All components in your pictures are for GAS Functions ONLY on the 3E Version (outside compartment)
*AC components are under cover on backside of tank
Atwood 3E Version was last used in 2003
It used 12VDC for Gas Function and the Electric was separate with 120VAC direct (own set of 120VAC T-stats)
*Sounds like the RV MFG installed a Control Switch inside RV for the AC as the OEM switch is on backside of Tank