Ahh, alright, with a little more research I've managed to do it, thanks
Now strange stuff is happening:
fyi: I've added a additional row to your getChildren snippet to allow an "empty" value, which doesn't seem to cause the problem:
$output[] = 'None.' . '==' . 'false';
Apparently the getPagetitle doesn't just replace the ID with the Pagetitle in the grid, it also replaces the variable itself.
If I output the ID in the frontend with the renderChunk (with the snippet call) deactivated it displays the ID.
If renderChunk is active it displays the pagetitle in the frontend.
If renderChunk deactivated it displays e.g.: "20/false/30". And I can choose between "None./Name_Of_ID_20/Name_Of_ID_30". Which is correct.
If renderChunk active: it displays "Home/Home/Home". I can choose between "None./Name_Of_ID_20/Name_Of_ID_30/Home", but Home always gets automatically selected.
I hope this explanation is unerstandable and I appreciate your efforts