Have you bought your airline tickets? What's your departure point from Europe?
Do you plan to make this trip without rental vehicles? You shouldn't plan to pick vehicles up in one country and drop them in another; the international drop charges would probably be exorbitant.
Go to the Deutsche Bahn website for rail travel times from Graz (nice city, quite non-touristy) to the other places you've mentioned. In some cases there are no trains, so you can Google "bus Ljubljana to Rovinj", etc.
I've been to all your potential destinations except the Alps, and they're all great. The Option 1 list may be too long for the time available. Check the travel times from point to point (Deutsche Bahn for trains, ViaMichelin.com for driving).
Budapest is, for me, a 5-night kind of place. I wouldn't go lower than 4 nights. It has a lot of varied attractions that are scattered, and it's a very pretty city for simply walking around.
I'd want 3 nights in very appealing Ljubljana; add a night if you prefer to day trip to Bled rather than relocating there for a night or two. You can stroll all the way around Lake Bled in 2 hours or so, so if you don't plan to go farther (such as to Lake Bohinj), Bled is an easy day trip from Ljubljana. Bled the town is really not all that special.
You really must have 1 night at Plitvice because the park is absolutely, mind-blowingly swamped during day-tripping hours. Not spending the night guarantees a severely degraded experience. You should try to get there by mid-afternoon so you can begin exploring the park as others are leaving and finish up early the next morning. There are public buses from Zagreb and Split. They have worked for me, but I wouldn't take the published schedules as gospel. I believe there are multiple bus companies operating (at least from Zagreb), which doesn't make things easier to pin down. Getting to Plitvice would be simpler with cars of your own and would allow you the freedom to book lodgings outside the park. Word is that the park hotels are rather mediocre and somewhat overpriced. However, it is also reported that, if you stay at one of those hotels, your one-day park ticket will be endorsed for free entry the next morning. (I haven't seen that documented on an official website, however.)
Istria is very attractive, and Rovinj would be my choice of base there. There are no trains in Istria, and bus service is rather infrequent, so it can be a challenge to fit Istria into a car-less itinerary. Once there, you can take buses (I think not terribly frequent) to colorful Porec, Pula (Roman ruins that seem not to be outstanding) and Vrsar (a cute hilltop town on the coast). I enjoyed the inland medieval villages of Motovun and Groznjan, which I saw on a once-a-week bus tour. With the transportation challenges in this area, it would be a good place to consider arranging a private van tour to places you would like to see.
Your group would probably enjoy seeing one of the cave systems in Slovenia. The Skocjan Caves are a bit more natural than the very-developed-for-tourism Postojna Caves, but either would work. There is some walking involved for both. Both have public transportation (or did, at the times of my visits), but for Skocjan you might have something of a walk from the place the bus drops you off. There are, of course, tours from Ljubljana, but your group is so large that I would explore private transportation. When I visited Slovenia in 2015, I found it not rock-bottom cheap, but I was pleasantly surprised at the cost of a taxi from Bled to Ljubljana, Lake Bohinj and Vintgar Gorge.
Vintgar Gorge would be another good side trip from Ljubljana; I think you can get there by bus after connecting in Bled, but I'm not sure.
Zagreb is a very handsome city that I like a lot. I was able to fly from there to Washington-Dulles with just one transfer.
