There is a wedge that holds the barrel on, a few inches ahead of the trigger. It's easy to see in the photos. That passes through a fitting that is soldered to the barrel. Put the hammers on half-cock (pull them back until you hear the first click), then remove the wedge by pushing it from the left side of the gun (pointed away from you, like you are going to shoot) toward the right side. I should come right out, but may have to be tapped on, gently, with something that fits in the hole but contacts the wedge. Be careful not to damage the stock any further. It has already been messed up some. Once the wedge is removed, you should be able to lift both barrels up and out of the stock, away from the hammers.
You really should take that gun to have someone look at it. If you have any way of showing who owned the gun historically, that would help a lot.
It looks like it was a pretty cheap shotgun for the period it was built in, but is a nice looking primitive, at least. Thankfully no one has taken a wire brush to it, or ground on it or sanded the stock or something stupid like that. It has the nice patina of age.