The 2" diameter is at the muzzle or the breech? If the cascable is really 1" diameter, it looks like the breech diameter is close to 3". 1.125" bore in a 3" breech is close enough for me if it is a steel barrel. The 3:1 ratio is for the area that has to contain the explosion, not the whole length.
OK, starting from the back, the 1" protrusion is called the cascable (or cascabel), the ring is the breech ring and the breech is the area just in front of the ring where the powder sits. At the absolute front is the muzzle and just behind is the muzzle swell. The area in front of the breech is called the chase. In your barrel, there is not a definitive point where the breech becomes the chase. In more ornate barrels, there are several other regions with bands that separate them so the names are more definitive.
One more question--what material is the barrel made from? If it is steel, I would ream to 1.5" and insert a liner with a .75 cal bore so you could use a standard muzzle loading round ball as shot. If brass or some softer material, then a .50" bore and use .495 balls.