Carol, you could certainly take GoOpti - I used them last fall to get from Ljubljana to Venice Marco Polo Airport (about three hours). It's probably half of that to get to Trieste. But you could take GoOpti all the way to Venice Mestre station and then take a quick regional train from there to Padova. You could take GoOpti all the way to Padova, too. I myself would think like you and want a shorter van ride and a longer train ride to Padova, so going through Trieste makes some sense, just more uncertainty. GoOpti charges less if you can be flexible on your times - and if you are taking a train from Trieste, you'd probably want to take a fast Frecciarossa...which costs a lot less if you book in advance, but if you miss it, you can't just take the next one.
Taking GoOpti directly to Padova would be simplest - if you don't have to be there at a specific time. If it's a lot cheaper to take it to Venice Mestre for some reason (since probably more shared ride passengers would be traveling there from Ljubljana,), you could just take a cheap regional train (no need to book in advance) from Mestre on to Padova.
Frlixbus does run direct buses to Treiste from Ljubljana, but you do have that uncertainty. I took one to Trieste from Ljubljana a few years back, and it was about an hour late, so I could not have relied on it to make a specific train connection.
If you love trains, you could take the train all the way from Ljubljana to Padova, but it would take an hour or two longer, and you'd have to change at least once, maybe twice.