I am writing a program that shows/hides the window of some target application. I was testing it out earlier and noticed something strange. If I run the target application as Adm
If you don't mind the window acting like you minimized it to the taskbar; You can, generally, show and hide windows from elevated processes by posting WM_SYSCOMMAND with a wParam of SC_RESTORE or SC_MINIMIZE.
This is by design. It is the lesser known twin of UAC, called UIPI or User Interface Privilege Isolation. An un-elevated program cannot commandeer an elevated one. Given the capabilities of UI Automation, this is an obvious counter-measure to stop programs from hijacking the capabilities of an elevated process. A security violation called a shatter attack.
Workarounds are to provide a manifest with uiAccess = true for a program stored in c:\windows or c:\program files and provided with a certificate. And for the target program to call ChangeWindowMessageFilter to allow certain messages to be sent. In your case that ought to be WM_SHOWWINDOW.