How would I replace this wall?
All exterior walls of the original building are load bearing. You can, however open up an exterior wall as long as you install a properly sized header to bridge the opening and support the header with jack studs. Depending on which way the floor joists (two story) or ceiling joists (single story) are oriented, you may need to install a temp support beam that spans the area where you are going to open up. This temp is installed before you remove any framing from the wall. Once you jack the temp enough to relieve any stress from the existing wall, you can demo the wall, build your header, support the header, then release the load down onto the header.  Fairly simple process, but must be sized and installed correctly.