How to restart the Dock without using the command line?

You can force-quit background processes using the Activity Monitor utility. Just find the Dock process (either sort the process list by name, or use the search field in the upper right), select it, then click the Quit button (the icon is an "X" in an octagon) in the upper left of the Activity Monitor window. It'll ask if you want to do a normal Quit or Force Quit.

No - the dock doesn't participate in the Force Quit window so you can't get at it directly.

You could easily take your AppleScript or shell script and wrap it in a launcher. Platypus app is my choice, but Automator also works:

1. Open Automator
2. Make a new app
3. Call it Dock Killer
4. Add one item to the recipe - Run Shell Script
5. enter killall Dock
6. Save the App to wherever you wish.

Now you can use Spotlight, Launchpad, FastScripts or any other manner of automation tools to use the keyboard or shortcut keys to launch your Dock Killer app. The free apps will work just fine, but I prefer LaunchBar for this task.