Engine Idling rough until engine warms up

We been having a recurring issue we backfired and the idle was rough and vibration in the vehicle, since check engine light was already on we had a Bank 1 Sensor 2 problem, (wire got tangled on the drive shaft and ripped out of the sensor). Got that replaced and reset the ECM to clear the code and to let the computer know the sensor had been replaced. Okay so she does fine if I let her warm up long enough to go in closed loop and we can drive her, but the OBD2 reader (still hooked up to vehicle to keep monitoring it) gave some interesting feedback when I tested all sensors wile my hubby was driving. OBD Module voltage 14.4V, DTC count 0, Misfire: Passed, Fuel System Passed, Components Passed, Catalyst :Not passed, Evaporative System Passed, Oxygen Sensor : Not passed, Oxygen Sensor Heater Passed.

We also have done a complete tune up. New spark plugs, replaced fuel pump last year after a similar problem (shop replaced it before testing the old one which turned out the old one had nothing wrong with it).
Shop had cleaned the distributor cap, after which it was running again not great, but not losing power either.
So yesterday we replaced the distributor cap and cables as well as rotor to complete the tune up. It is still doing the same as before replacing the O2 Sensor or similar.
My husband dropped me off at work after letting it warm up to go into closed loop, but he had to make stop somewhere for a while with a busy parking lot so he was unable to let the engine warm up enough to go into closed loop and the engine backfired several times and engine revved up so he pulled over and let it idle for about two more minutes after which the RPM went to normal idle than low back normal than low, but no more backfires. A few more minutes later he was able to drive normal with no issues. I am out of Ideas.