Refilling AC before at least one leak is found and fixed is an apparent waste! Make sure your AC specialist provides a warranty: it's quite likely you'll have to return.
Blowing hot air instead of cold. An "old school" trick to release the heat burden on the overheating engine is to turn the cabin heater on. This may be the next step (after disabling the air cooler) the computer can take as well.
But there must be errors/warnings logged, of course! If none it must be not the case.
Replacing a pump when they aren't sure it's faulty (it can be the controlling sensor instead) looks an apparent bullshit.
Going fast doesn't necessarily mean the engine is hot: it's being cooled with the oncoming air. Just make sure you aren't revving high (constantly).
It's quite more likely to get the engine overheated in a traffic jam. In frosty weather you might need to go slower to keep the temperature up (and/or close the holes on the front end of the car), by the way.
The "Eco Pro" driving mode should be handy to keep the engine temperature down.