Ljubljana day trip to Lipica?

I haven't made that trip, but there are trains as far as Divača, from which it would be a fairly short taxi ride to Lipica. I do not know where the stud farm is located vis-à-vis the town of Lipica, however.

You can check train schedules on the Slovenian railway's website.

I'm nearly certain there are day-tours by bus from Ljubljana to the stud farm, probably only on the days when the activities you cited are occurring. The trips may include a visit to one of the cave systems (Postojna or Skocjan), and I'm not sure you'd have as much time as you'd like at the stud farm.

No personal experience getting to Lipica by public transport, but there should be bus service between Sežana and Lipica. Getting to Sežana is easy as it’s the terminus of many southwest-bound trains from Ljubljana. I would probably opt for the car rental, though, seeing as you are bound by the performance schedule and coordinating train and bus times can be a hassle. Plus, you can explore the Karst countryside with a car. You can visit places like the hilltop village of Stanjel or the Rakov Skocjan natural monument along the way.

I’m not sure why the RS guidebook indicates that most central car rental offices are closed on Sundays, they are not. Avantcar’s city centre office is open until 2pm on Saturdays and Sundays, Sixt until 2pm Sat and until noon Sun, Hertz and Europcar have similar hours. I’m sure you can arrange to return the car in the evening for an extra fee or just keep it overnight and return in the morning. All the companies I listed have their city centre offices in the area between Grand Hotel Union and the central railway station.

Be careful re late April, April 25 to May 3 are the spring school holidays, places like Lipica or the caves will be busier than usual. Pay attention to opening times as April 27, May 1 and May 2 are all public holidays. Most stores and all supermarkets will be closed, as will all shopping malls, some restaurants as well, etc.

Google shows a Europcar location near the train station that is open Sat 8-1 and Sunday 8-12. I would try entering a booking, using AutoEurope, and see if this time shows as open. If they are, you have your choice of events to attend on either Sat or Sunday. Just take a taxi to/from the car rental location. Driving in Ljubljana isn’t bad. From the train station it’s pretty simple to get to the freeway.

I rented a car for the day from Avantcar in Ljubljana in 2017 from the city center location and returned the car after hours in the secure parking lot and then left the keys at the front desk of the neighboring hotel. All the car companies should allow something similar. Yes, driving in Slovenia is easy. (If you've not rented a car in Europe before, be sure to have the collision/CDW insurance thing figured out before you get to the place to rent the car. Some credit cards offer this coverage as a benefit; I kind of got screwed by that - not with Avantcar - once and would be kind of gun-shy about using that again. When I rented with Avantcar just for the day, it was easiest just to accept the full insurance and not worry about it.)

If you are renting a car for the whole day, I would make good use of it and do more than just Lipca. I'm not sure what the tour includes, but there is a lot to see that might not be on the tour - check out the Rick Steve's book obviously. Piran on the coast is an adorable Venetian seaside town. There caves too of course. There is Lake Bohinj and surrounding area, which you may not get to see otherwise. I've written a few times here about the beautiful scenic drive from the town of Skofja Loka through the mountains via Jamnik and Kropa, so you could do that too and also stop in a few of the towns.

If you have a few days, and the tour will have time in Ljubljana anyway, you obviously spend time elsewhere outside of Ljubljana, though it's a lovely town, and more nights there is probably not a mistake if you like it as much as I did.

When I visited in the fall of 2017, there was an Avis counter inside the Grand Hotel Union Business, in the center of Ljubljana and just steps from the main tourist area. The hours are showing as 8-Noon on both Saturday and Sunday, though I would definitely confirm that directly with the local counter; we've had cases where the US information on hours was not accurate.

I was driving from Trieste and drove to the stud farm in Lipica and to the Skocjan caves, which are less than 15km apart from each other. We took the informative guided tour at Lipica Stud Farm (the site indicates this is 8x / day, April - October) and saw the horses up close in their stalls and corrals. Afterwards, we wandered the expansive grounds for an hour or two, admiring the horses around the grounds.

(Drat, I was going to tell you about a delightful restaurant nearby, but I see that it has permanently closed.)

The driving in Slovenia is easy and beautiful. We used Google Maps (downloaded for offline use, I didn't have a data plan on that trip) and it worked perfectly.