I don't think we can tell them how to take their vacation days but if they are not following the manual in getting them approved can't we deny the request and use that to take action? I have trouble comprehending how we can call it an unexcused absence yet they get paid to be off.
Do you have to call it unexcused? Call it unapproved or unscheduled, which speaks directly to the policy violation and would avoid any confusion about whether it was a paid day off or whether the supervisor said "OK" when they called in to say they weren't coming to work that day.
You said you discussed and documented previously. If the line was not clearly drawn to where you are comfortable with disciplinary action at this point, I'd say take this opportunity to make it crystal clear and punish the next offense.