Route from Ljubjana(Slovenia) to St.Moritz (Switzerland) via Italy.

There is a "direct" train between Ljubljana and Trieste but you need to change train at the border station Villa Opicina. From there, you can use a old Tram to the city instead of the train (not incl. in Interrial).

In your case I would look to stay one night in Verona or Bergamo. I would go on the line between Bergamo and Lecco (one part has rail replacement) and then to Tirani.

I can only find 1 direct train from Ljubjana to villa opicina and that one leaves way too early (5:30). And a late connection with a 1hr change in sezana.

Last time i traveled from Trieste towards Ljubjana there was atleast still the replacement Bus from Trieste to Sezana.

There was a thread on Trieste - Villa Opicina trains some months ago in this forum. Different timetables/route planners had given dfferent informations on cross boarder trains from Sezana in Slovenia to Villa Opicina in Italy. If you make it to Villa Opicina and there is no connecting train to Trieste Centrale you may walk about 15 to 20 minutes to the town centre of Opicina and take the Opicina Tram down from the karst plateau to Trieste as suggested by ​@Angelo. Or you find a bus stop in the via di Prosecco and take a bus (usually route 4) to the Tieste city centre. Twice a day or so bus 4 makes a detour and calls at the Villa Opicina station to connect with a train.

A connection from Ljubljana to Italy which is for sure working is via Nova Gorica, Slovenia and Goricia Centrale, Italy. That two stations are connected by bus INT (from the backside of the Nova Gorica station) and Gorizia city bus 1 wich can be reached by walking across the station square and the boarder in the middle of the square. From Ljubljana Nova Gorica can be reached by train either via Sezana or via Jesenice in about the same time. Of course it is a detour to go to Trieste via Nova Gorica and Gorizia.

​@Andreas1099 good idea with Nova Gorica. You can use on weekends the direct regional train Nova Gorica-Venice.

There should also be a direct afternoon/evening train. Check Ljubljana-Villa Opicina on https://potniski.sz.si/en/ and Villa-Opicina-Trieste on trenitalia.com, or mention your travel date.