Getting from Croatia to Trieste, Italy?

I'm sorry, but I don't really understand what you are trying to do. Are you planning to spend time in Trieste, or are you heading somewhere else? I assume you are heading up the Dalmatian Coast - are you going to Istria? Slovenia?

We will definitey take our first rental car around Croatia, including Istria. We will then bus to Trieste where we'll pick up another rental car and spend a week in NE Italy.

Correct, the bus connections are limited, there is no train between the closest border crossing and Trieste, and there is a third country in the way.

For summer ferry schedules, see http://www.adriatic-lines.com/524/EN.

If you take a train from Sezana, Slovenia to Villa Opicina, Italy, then you can take the Villa Opicina to Trieste tramway. From Rijeka to Sezana still requires an additional train and bus, according to train schedules. You could also play with Rome2Rio.com to locate other buses.

I know you're trying to avoid drop-off fees, but perhaps check whether a drop off fee in Slovenia would be less daunting than one in Italy. In the past, I took bus one way from Trieste to Portoroz (not on Sundays) and taxi on the return, when visiting Slovenia.

Thank you very much for your information!

We took a bus from Rijeka to Trieste a few years ago, so that might be a good place to drop your car. It's a 2-3 hour bus ride, which left Rijeka in midafternoon. Not sure if that's still the current schedule.

In Trieste, there's a travelers information office at the train/bus station with a hotel-finding service that was very helpful, and lots of hotels within walking distance.

There are several trains daily from Trieste to Venice, if you want to wait to get your car in Venice.