You are using the wrong function i.e. CInt should be CDate like so:
Code
Option Explicit
Private Sub Txt_Depart_AfterUpdate()
Dim textYear As Date
Dim textYear2 As Date
textYear = CDate(Me.Txt_Arrival.Value)
textYear2 = CDate(Me.Txt_Depart.Value)
If textYear > textYear2 Then
MsgBox "Departure date is before arrival date"
Exit Sub
End If
End Sub
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I believe you also had the Exit Sub in the wrong spot.
HTH
Robert