You say the radiator fans work but those conditions sure sound like you aren't getting airflow when stopped.
I say this based on your symptoms:
- Cooling goes down to zero when the car is stationary, starts to cool after the car has been moving for some time
When stationary you are relying on the fan(s) to move air through the condensor to keep the system cool
- It doesn't cool enough during the day (~ 35-45 °C ambient temperature)
This part shouldn't be fan reliant so there may be some other impacting issue also such as low pressure, damaged condensor or undersized condensor for the ambient temperatures
- It cools quite well at night (even when stationary)
At night with the lower temperature, even stationary, the condensor may be getting enough cooling performance just from the ambient air and so lack of operating fan wouldn't hurt it
- It is ice-cold five minutes into continuous driving at night.
This is the ultimate perfect conditions for it, cool air rushing into the front of the car because you are moving, no fan needed
There should be an electric fan that is turned on when the A/C is running.
Start the car, get it up to operating temperature and turn on the A/C.
Then check to see if that electric fan is running.
If it isn't, there may be a wiring issue or an issue with the fan itself.
If it is running, then you need to look at other areas.
You said you replenished the R134a, was this with a do it yourself bottle or did you take it in? If done yourself, you may need to take it in and get the pressure checked, make sure there isn't a refrigerant leak. If you took it in, talk to the shop, find out if they pressure tested the system, if not, then the same issue may apply.
Perform a visual inspection of the condensor, make sure there isn't a large section of bent/damaged fins. Some is ok, it is going to happen, but the more that are damaged the lower the efficiency of the condensor.
Check the tension of the compressor's belt. If there is a significant change in ambient temperature between day and night for you, then with heat soak the belt may be getting just loose enough where it is slipping and not turning your compressor as well as it should. If the belt hasn't been changed in a while, consider doing it as it is relatively cheap.