First make sure you understand Module before using DynamicModule. Once you understand Module, understanding DynamicModule can thought of as a version of module that works with Dynamic.

The first argument to Module are the variables to be localized You'll also probably want to initialize them.

DynamicModule[{coordinaten = {}, kortsteTourIndex = {} , kortsteTour = {}},

If you run into a problem like this, first try solving a simpler version of the problem. The example below shows an Interface that records the points you click on it:

DynamicModule[{coords = {}},
 Dynamic@EventHandler[
   Graphics[{Point[coords], Line[coords]}, PlotRange -> {{-1, 1}, {-1, 1}}],
   {"MouseClicked" :>  (Print[coords]; AppendTo[coords, MousePosition["Graphics"]])}
   ]]

For this kind of interface, you might also consider using ClickPane.