PCS-ing to Casey Korea. Can I fly my family out-of-pocket and have them live in Seoul?

My family where command sponsored in Hawaii, and they are currently command sponsored here in fort hood.

So who will pay for my wife and kids to stay in the states? I thought the Army will have to pay for their housing? Korea will be my third duty station in the army and I have never had this problem. From what I hear you guys are saying, I have to pay out of pocket for my family housing either in Korea or in the states? If they stay back in be states they have no where to go.

Of course you can.... however, if there are no command sponsored then you will have to pay for their logistical support, i.e. rent, medical, etc...
Additionally, I believe that then can only live in there for a couple months as a "tourist" after that they will have to get some sort of visa if they want to stay any longer.

Strictly speaking, I don't believe there's anything stopping you from doing so but you should check with your gaining unit before doing it. I was stationed at Camp Stanley a few years back and we had some people fly their families in without command sponsorship. One issue they ran into doing so was the chain insisted that they stay in the barracks rather than with their families.