Bonnie, I've found driving on Croatia and Montenegro (and Bosnia) very easy. Zagreb to Plitvice is a piece of cake, unless you are from one of the countries where you drive on the other side of the road like the UK, etc. End of September isn't high season anymore, so you shouldn't have much traffic. But yes, I would definitely overnight at Plitvice, even in September, if you can. But this makes sense only if you plan to get up early enough to enter the park at 7am-ish when it opens. If you are not an early riser and can't get up that early, then you will probably not beat the crowds anyway...so you might as well just day trip from Zagreb anyway.
If you stay at one of the overpriced but convenient park hotels, one benefit is that they can stamp your park ticket from the day before so you can enter the park a second day without paying again. But the park is so popular now that I hear these hotels sell out early; if you will visit this coming September 2018, it may be too late to get a reservation at one of the park hotels. Should be plenty of Sobe (B&B's) near the park, though.
In 2015, I drove from Dubrovnik to Kotor (spent one night there). I used the alternate "Konfin" border crossing to avoid possible backups at the border; the Konfin crossing can't handle tour buses, so you shouldn't have any delay there, though it is a bit of a detour. I had only one car in front of me, but I had to wait five minutes for the guard to make a phone call before he talked to me.
Otherwise, driving along the Bay of Kotor offers breathtaking scenery. I am glad I drove so I could stop and take pictures in numerous places (including a stop at the town of Perast, highly recommended). I found no need for a guide at all. However, for me, the highlight of all of this was the Bay of Kotor and the views, not the visit to Kotor itself. It was a nice town (walk up the "walls" above, for breathtaking views down on the bay, worth the steep climb), but not as amazing as say Dubrovnik in my view. So I wouldn't think of it as "trip to Kotor to see Kotor." This is a case where the journey is the destination.
Just make sure you rent a car that allows leaving the EU (Croatia is in the EU; Montenegro isn't even though, curiously, Montenegro uses the Euro as its currency but Croatia doesn't). You need an insurance card for the car, and that probably will add something to the cost. Not every rental car comes automatically with the right insurance card, so ask for it ahead of time!
Another amazing drive was from Kotor up through the mountains to the town of Cetinje (there's a round-about faster route not through the mountains; not scenic, which would defeat the purpose). The twisty, scenic route has many switchbacks which might frighten you, but I had no trouble driving it. I just took it easy. I stopped numerous times for pictures down. I wouldn't try to squeeze in this drive though if you are doing Montenegro only as a day trip, in late September when the days are getting shorter. Just stick to Kotor and the bay below.