Please excuse my naivety - this thread freaked me out a bit as I have very little international travel experience. My family of 4 (US citizens) are booked on DL award tickets from the US to AMS-FCO-MLA. Because the final leg required an overnight stay that I didn't really want, I recently booked Air Malta AMS-MLA with cash, intending to just use that flight and not board the AMS-FCO (on Alitalia). I'm assuming I won't have any issues like the OP here, but wanted to make sure.
TIA