Hi!
If you had more time I would suggest booking a tour with the travel agency. There are many great agencies in the town center, but the problem is that the tours start around 7 am and you´re back in Split around 6 pm. They usually consist of visiting the local places as well, such as Stiniva, Komiža, Budikovac Bay, etc.
If your budget is not strictly limited, the four of you could rent a speedboat and go with a skipper. It takes around an hour and a half to get to the cave, but later on, you can go where you wish.
Whichever option you choose, note that the Blue Cave is only open in the morning and you can not swim in there. You spend only about 20 minutes inside, so don´t establish your whole trip on it.