I built a gate using the following tools: fire axe, hammer, pliers.
Once the gate was fully assembled, the area to trigger "open gate" prompt was not accessible. Neither the hammer or fire axe have the ability to tear down the fence from the inside.
I believe the "open gate" promt should be accessible from anywhere inside. Also, a fire axe should be able to disassemble a wooden fence/gate(realistically they can).