The OP is right to a point.
Of course a station can be oriented so it both mirrors tidal locking and axial rotation, angular motion with respect to perpendicular axes is independent, you can spin in 3 directions if you want.
No, when you've set the station rotating with an axis pointing at the planet then that axis is fixed from that point on. If you start adding another component of rotation it sets the total angular momentum with a new axis - it doesn't start rotating the previous axis of rotation.
Edit: well it gets kind of complicated when you're trying to figure out what's happening in some cases like torque free processions but I don't think you can get the station to behave in the way you want.
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