1. Heater valve wide open changes temp around 5-10 degrees
2. The odds of the temp door moving on its own are slim but don't say cant happen but, if it moves will make a big change.
3. Compressor turning off for some reason makes huge change in temp.
4. Refrigerant level changing temp that far is not going to be erratic.
5. The possibility of having two or more problems is very possible.
6. Weak fan clutch will cause pressure to rise shutting off compressor. (see #3)
Start by eliminating things as possibilities, easiest first.
Refrigerant pressures are read at High Fan, around 1500 rpm. Look at gauges. Highest High gauge reading and lowest low gauge reading.
The High pressure will be based on ambient temp (around ambient X 2.4 ish), low will be 15-25 psi and compressor will start cycling off if the low gauge starts dipping below 20 for a length to keep evap from freezing. This is normal.
"IF" the low side is running close to 30 psi, TXV valve is weak.
"Low" high side gauge reading means charge is low.
"High" high side gauge reading means too much refrigerant or, more commonly, fan issue. The high side safety switch will shut compressor off. Weak fan clutch is common here.
Run temp control to full cold. Go to heater valve. Look at cable attachment. Push on cable and see if the valve is closing all the way. If its open 1/4 of an inch that's around 10 degrees more in vents. I commonly have to adjust these.
"When" the issue happens again, look at compressor. Did it turn off? If it did, something is shutting it down. Controller, wire, relay, connector......
"IF" the compressor is still running when it happens, you eliminated a power problem.
These are a few basic steps to try to narrow down the issue. Intermittent problems are a pain.