I like to keep everyone updated, this is what I ended up doing:

Code:
Declare Function ShowWindow Lib "user32" (ByVal hWnd As Long, ByVal nCmdShow As Long) As Long
Declare Function EnumWindows Lib "user32" (ByVal lpFunc As Long, ByVal lParam As Long) As Long
Declare Function GetWindowText Lib "user32" Alias "GetWindowTextA" (ByVal hWnd As Long, ByVal lpString As String, ByVal nMaxCount As Long) As Long

Public lngOutlookHWnd As Long

Public Function EnumWindProc(ByVal hWnd As Long, ByVal lParam As Long) As Long

    Dim strTitle As String
    Dim lngTemp As Long
    
    strTitle = String(255, 0)
    lngTemp = GetWindowText(hWnd, strTitle, 255)
   
    If Left(strTitle, lngTemp) = "Microsoft Outlook" Then
        lngOutlookHWnd = hWnd
        EnumWindProc = 0
        Exit Function
    End If
    
    EnumWindProc = 1

End Function
Public Function GetOutlookHWnd() As Long

    EnumWindows AddressOf EnumWindProc, 0

End Function

Public Function EmailIntro(lngContactID As Long)

    On Error GoTo Error_EmailIntro

    Dim appOutlook As Outlook.Application
    Dim miMail As Outlook.MailItem
    Dim rsIntroEmailInfo As DAO.Recordset
    Dim strFileName As String
      
    Dim lngTemp As Long
      
    Set appOutlook = New Outlook.Application
    
    'Make sure Outlook is shown and maximized
    GetOutlookHWnd
    ShowWindow lngOutlookHWnd, SW_SHOWMAXIMIZED
        
    Set miMail = appOutlook.CreateItem(olMailItem)
...
ETC

Basically, I enumerate the windows to find the window with the text "Microsoft Outlook" then I set that particular windows hWnd to a global variable, which I pass to the ShowWindow function.

Thanks anyways guys!