I'm not sure what you mean by "join sheets organized by the day", so let me know if my answer does not fit with what you're trying to do.
When you set the time properties for a layer, if will ask you if your data has a start time field or both start and end fields. You then go on to specify the interval you want ArcMap to step through the time field(s). So I believe the answer would be that you should combine all of your case data into one table, making sure the date fields are truly designated as type = date. ArcMap should be able to then help you visualize the data however you want over time (days, hours, minutes, etc...)