Croatia - 10 day itinerary with kids

Some people take very long day trips from Dubrovnik--to Mostar or Kotor. I consider both too much time in a car for one day. I would look at sea excursions you could do like a boat trip to the Elafiti islands. You can also do kayak trips. The small island of Lokrum is just offshore and offers good swimming and views of old town.
In Korcula, we enjoyed Lumbarda. In addition to the beaches, you can rent bikes and ride through vineyards (or parents can do a wine tasting while the kids enjoy that).
From Split, there are several islands day trips you can do--Brac or Hvar or even tiny Solta. In addition to Trogir, you might want to visit Sibenik and see its cathedral or go to Krka park.

Since it is August, I would book boats the day before.

We did the same route this past September. I always like to book the ferries ahead of time just so it is one less thing I have to worry about. Anything I can book ahead of time which we know is a definite, we book. The cost is the same either online or at the port. You can see the routes and times at Croatiaferries.com then go to Krilo.hr to book and print the tickets. They also accept the tickets on your phone. I’m old and like to have printed copies. There is usually one, maybe two ferries for each route, one early, one late afternoon. Avoid Jadrolinija, they are much slower and not as nice. Krilo uses catamarans. When in Dubrovnik, take the local ferry at the port in the old town to Lokrum. It is a nature preserve and has a nice beach on the opposite side of the island, they also have a lovely cafe, only one there, or you could bring a picnic. If you are going to go to Banje Beach, go early in the morning. Besides the fact it gets very crowded, it gets oppressively hot. We would be on the beach by 7:30. Tell your kids they can take a nap later or sleep when they get home.

Tip: purchase small inflatables and bring with you as these items are well overpriced in Croatia. Most beaches "sand" are pebbles so consider bringing lite swim shoes with rubber soles to help with pebbles.
Split has very nice public beach, Bacvice Beach, and is 10 minute walk from Old Town. This area also has several excellent BNB's offering excellent value and local restaurants.
Dubrovnik is most expensive of all towns in Croatia. Recommend travel via ferry, a great experience.

It sounds as though it’s too late if accommodation is booked, but I would spend a night less in Dubrovnik and add this to Korcula.

Trogir is an excellent day trip from Split. Plitvice will be very busy in August and it’s better if you stay there so you can get into the park as soon as it opens.