Hm sorry maybe I’m misunderstanding you, but it looks to me like you’re already doing exactly the right thing, you’re already exporting a track, otherwise you wouldn’t have the red dotted line 
As you mention, the IMPORT back into kurviger is probably what’s tripping you up. Note that kurviger will ALWAYS calculate a route, based on its algorithm (and yes, OSM), that’s its job. Kurviger takes the data that it finds and then… Well… Generates a curvy road
I bet that when you take your exported track and upload it to a TomTom it would work as you expect. On a kurviger map it won’t, at least not until this feature request is done: App / Website: Straight-Line / Point Planning mode / Plotting a track on unsurfaced roads