12/2 is not going to cut it. This is what I would do. I'd measure the distance from the panel to where your going to put the subpanel. I.E 50 feet, add 10 feet because you will need it. You are going to need a 8/3 wire for an 40 amp subpanel. If not you will pop breakers all day long. Start at the panel and disconnect the wires leading to the outhouse and duct tape the new 8/3 wire to the old wires, now go to the out house and and disonnect the out and get to the wires. Start pulling the wire until you get your new wires. Wire up your subpanel and the go back to your panel and wire that up. This is provided that your wire is ran in conduit under ground like it should be per N.E.C