Oh ok, now i get it. So one batten at far edge of each building side to create a sort of L shape housing at the external corner, then a square section timber fitted to that L housing, fastened into one or both of the battens. And finally the cladding. Got it. Thanks.2x2 will normally sort if it is 20mm cladding and 25mm batten.
You can screw into the batten rather than the edge grain of the cladding.
Or you can get capping that goes over the top and covers end grain.