I don't think the longitudinal shear is an issue either, you have the same force more or less (depending on reinforcement forces) a little bit round the corner, and a little bit further along the wall a similar longitudinal shearing force. Why is the corner so special? Generally you would expect it to be checked at vertical interfaces between pours, checking shear friction, etc.
Do you check the longitudinal shear force in a monolithic beam shearing horizontally along its length because it has to transfer the top compression to tension at the bottom? Don't think this scenario is any different in principle.
I prefer to look at the entire core for moment capacity, for compatibility you have to (i.e. define pier for extracting moment and axial load for all walls comprising the core). For shear in individual walls you need to define piers on all walls, and check the shear taking into account the axial load in the individual wall pier. As 'flanges will either be in tension or compression. I've seen people design as three separate joined piers but the results are sometimes very odd. Run the inbuilt design tools in etabs with both scenarios and its unlikely you will see the same longitudinal reinforcement for example. Not that I'd trust the layout to etabs at all, prefer to extract forces and use other tools to do the design.
If you are interested in the vertical longitudinal shear, setup section cuts to read this force off straight out of the analysis at the corners, its the only way I know of. Just setup some simple models to get the hang of it and get your head around the sign convention and which valuer is what shear/moment/axial load as its not the most intuitive output to understand.
