Private Sub TextBox1_Change()
[a2].Formula = CDate(TextBox1.Value)
End Sub

Private Sub TextBox2_Change()
[a3].Formula = CDate(TextBox2.Value)
End Sub

Private Sub UserForm_Initialize()
TextBox1.Value = [a2].Text
TextBox2.Value = [a3].Text
End Sub

TextBox1.Value = Format([a2].Value, "dd.MM.yyyy")

Private Sub CommandButton2_Click()
    If [a1] >= [a2] And [a1] <= [a3] Then MsgBox "fgh"
End Sub

Private Sub TextBox1_BeforeUpdate(ByVal Cancel As MSForms.ReturnBoolean)
    Dim dt As Date
    With TextBox1
        If IsDate(.Value) Then
            dt = CDate(.Value)
            .Value = Format(dt, "dd.mm.yyyy")
            [a2].Formula = dt
        Else
            Cancel = True
        End If
    End With
End Sub

Private Sub TextBox2_AfterUpdate()
    Dim dt As Date
    With TextBox2
        If IsDate(.Value) Then
            dt = CDate(.Value)
            .Value = Format(dt, "dd.mm.yyyy")
            [a3].Formula = dt
        Else
            Cancel = True
        End If
    End With
End Sub
Private Sub UserForm_Initialize()
    Application.EnableEvents = 0
    TextBox1 = [a2].Text
    TextBox2 = [a3].Text
    Application.EnableEvents = 1
End Sub