Patrick,
the “exported” URL is unigue for a given state of a route. As you find out, you may change the route but the URL points always to the version at export.
To share your route with others you need either the URL or a file (.kurviger or/and .gpx) both created via export.
I use files (never used the Kurviger cloud) - see Access web route from app - #9 by zaphod_42 - believe me, it works. If you take the same file name, it’s always the latest version. But you can even have several versions of the same daytrip (then of course with different names).