Windows Shortcut files allow applications to be started maximised, restored (normal) or minimized. As snapped to the left or right are additional temporary window states, why not add them as options in the application's Shortcut tab, Run property dropdown?
Extending WSH and .NET Framework programming objects would allow creation of shortcuts and control of running applications.
WMI, WshShortcut Object, WindowStyle Property
intWindowStyle values:
1 Activates and displays a window. If the window is minimized or maximized, the system restores it to its original size and position.
3 Activates the window and displays it as a maximized window.
7 Minimizes the window and activates the next top-level window.
Request for two extra intWindowStyle values:
x Activates the window and displays it as a window snapped to the left.
y Activates the window and displays it as a window snapped to the right.
.NET Framework, System.Windows namespace, PresentationFramework assembly, WindowState Enumeration:
Maximized, Minimized, Normal
Request for two extra WindowState values:
SnappedLeft, SnappedRight