setOvercast, setRain and setFog only effect the local computer, their effect is not transmitted over network.
So you need to signify the weather change in your trigger by a variable that you publicVariable, and ONLY THEN, with another trigger that awaits this variable change, you will change the weather.
This way, when condition are met (which can be true on 1 computer only, meaning the weather changes would only be done on this computer), the variable is broadcasted, and every computer see the variable change and change the weather accordingly.
So, your radio alpha trigger should have code changeWeather = true; publicVariable "changeWeather"
And you have a second trigger with condition changeWeather
and with code 0 setovercast 0; 0 setrain 1