I would skip Brno in favor of Cesky Krumlov and probably more time in Prague.

From Brno to Prague - forget car or bus, because the main highway connecting these two cities is under heavy reconstruction. This and summer traffic makes for extremely unpleasant conditions on the road. Train would be much more pleasant and faster option.

I would just fly (or take the train) from BUD to PRG and make a car trip to Cesky Krumlov, completely skipping Brno. Much more things to do and see in or around Cesky Krumlov than in Brno. For example visiting the beautiful castle in Hluboka nad Vltavou or enjoy activities at Lipno lake.