Stalling

Your description sounds like the canister purge solenoid is stuck open. When it's running and you open the fuel cap it is creating a large air leak, then when you fill the tank with fuel it is acting like it is partly flooded due to the extra fuel.

Replacing it isn't that difficult, you need to get the left front wheel off, then remove the inner wheel well liner. The valve is mounted to the side of the engine block down about halfway in line with the starter. It has one bolt that holds it to the engine 2 hose connections and the electrical connection. The toughest part is usually getting the bolt out if you're in the rust belt. The connectors are all quick connect type. Testing to be sure it's the problem involves removing the solenoid and blowing through it. In normal use it is closed, so air shouldn't go through if it's disconnected.