Stuck bathtub faucet stem
It looks like you have been wrenching on the wrong piece (the stem). You need to unscrew the entire assembly at the valve body. The body is deeper in the wall, if you shine a flashlight in there you will see where you need to unscrew it. It takes a special deep socket made just for that purpose:





The picture shows the person using a rod to turn the socket; you may need to put a pipe wrench on the socket to get it to break free. Ensure the water is shut off before you do this.

Pictures shamelessly grabbed off of the internet.