This issue intrigued me so I kept looking into it and here's what I've found.
In Windows 7 and newer, the shell (Explorer.exe) changed the behavior of the taskbar, and groups taskbar items (processes, files, windows, etc.) to make it easier to find what you're working on (and share features like the jumplists and taskbar preview). In order to do that, the shell needs a way of identifying what to group.It does this using the "Application User Model ID". (See https://msdn.microsoft.com/en-us/library/windows/desktop/dd378459(v=vs.85).aspx
The Windows shell uses some heuristics to try to identify what should be grouped but it isn't perfect. For example, for programs started via shortcuts, the target in the shortcut must be the same. So if you have two shortcuts to the same program but with different command line parameters, they would be considered different and not be grouped. For processes it assumes only processes with the same name should be grouped. And that's the situation with Emacs - emacs.exe and runemacs.exe aren't considered the same by the Windows shell and it doesn't group the icons on the taskbar and similar undesired behavior we see.
Microsoft says the way to solve this is to explicitly set an AppID which overrides the heuristics. So for better behavior in Windows 7 and later, all emacs processes (emacs.exe, runemacs.exe, emacsclientw.exe, etc.) should be modified to call SetCurrentProcessExplicitAppUserModelID() during their startup.
To use it locate the shortcut you have pinned to the taskbar and run this program on it. It's a command-line program, see the win7appid page for more. Pinned taskbar items are usually in <windows-drive>:\Users\<username>\ApplicationData\Microsoft\Internet Explorer\Quick Launch\User Pinned\TaskBar.
The AppId to use would be "GNU.Emacs".
I've tried it and it fixes things, and the David, the OP, confirmed it worked for him in a private email.