My CSS looks like this:
I found a solution which is working but far from perfect:
I added a
padding-right : 15px to my div, to automatically grow the entire div. Now if the vertical scrollbars appear, they fit within the padding so the horizontal width is still ok.
Regretfully the padding of course also shows up when no vertical scrolling is needed, making my div just a tiny bit wider than it would have to be... :/ Well, in my eyes this is still preferable to unneeded horizontal scrollbars.