Day/time never mattered much to me. I could deal with those changes (particularly since I honestly had no other way to go about it with my own crazy schedule). But my T was always very consistent in demeanor, approach, message, etc. which for me is really what is important. Life doesn't happen on a set schedule, but the people in our lives should be fairly predictable and reliable (not 100%, but even their changes are generally fairly predictable and understandable so they don't throw us). Your therapist seems very inconsistent in the areas that really matter to that sense of stability and safety in interaction. That would be something that would quickly rule out a therapist for me.