Press Left Shift while editing a transport line to snap to the track, instead of snapping to the station.
Note: When Left Shift is pressed, you need to hover on the tracks for the tool to show. You may be frustrated with the much-shorter snap distance. The aim of the next fix is to increase the snap distance so it becomes easier to snap to the track.
The Holstebro Double-track train station by conex is a well-made asset and the first example of a multi-track station:
By design, this mod should not break your save game. You can unload this mod at any time and still play your city.
The following mods may prevent this mod from working properly: