AutoHotkey has PostMessage and SendMessage commands that can send internal "messages" to windows or controls. Often programs use these types of messages for their menu commands. To find out the proper message values you need, you use a program like Winspector to log messages of possible interest.
For more information, see SendMessage Tutorial.
(This tutorial is also buried in the AutoHotkey help file: go to the bottom of the PostMessage/SendMessage page, and in the Related links, click on Message Tutorial.)
The program pictured in Barlop's question is Rainlendar.
Using the methods from the tutorial above, I made the following example AutoHotkey script that sets F11 to "Hide all windows" and F12 to "Show all windows".
WM_COMMAND := 0x111
SHOW_ALL := 598
HIDE_ALL := 599
DetectHiddenWindows, On
#IfWinExist Rainlendar2 Control Window ahk_class wxWindowClassNR
F11::
window_id := WinExist("Rainlendar2 Control Window ahk_class wxWindowClassNR")
PostMessage, %WM_COMMAND%,%HIDE_ALL%,,,ahk_id %window_id%
Return
F12::
window_id := WinExist("Rainlendar2 Control Window ahk_class wxWindowClassNR")
PostMessage, %WM_COMMAND%,%SHOW_ALL%,,,ahk_id %window_id%
Return
What app is providing that menu? – Doug Harris – 2010-12-17T18:27:29.607
What's wrong with Alt+Tab or (if the OS is new enough) "Windows key" + tab? Please give us more information like Doug Harris is talking about. – David – 2010-12-17T18:40:45.633
@Doug Harris Rainlendar. Can autohotkeys not do it? There is no minimize button, it uses one of those special skins.. and doesn't appear in alt-tab menu. there are probably quite a few apps like it. If there was a way to go through the menu as mentioned with a shortcut, that'd be a solution regardless of app. but if you know of another solution, that's not quite as good but if it works and there's no better one then fine. I don't mind you stating it in comment before knowing what app it is, since it may be of use to know. – barlop – 2010-12-18T02:16:21.680
@David it's not even in Alt+Tab see comment above to Doug. – barlop – 2010-12-18T02:16:53.223