If my wife lives in Brazil and I go to Korea, what is BAH based on if she ends up coming with me?

I'm in the Army, and I'm curious about volunteering for Korea...if my soon-to-be wife from Brazil moves out there with me and I'm unable to get command-sponsored to move her, do I use the OHA for Brazil even though I'm not stationed there? Or will I have to use the BAH rate for wherever I'm stationed in Korea and just eat the cost of moving myself?

I'm in the Army, and I'm curious about volunteering for Korea...if my soon-to-be wife from Brazil moves out there with me and I'm unable to get command-sponsored to move her, do I use the OHA for Brazil even though I'm not stationed there? Or will I have to use the BAH rate for wherever I'm stationed in Korea and just eat the cost of moving myself?

Oh, and if she doesn't move with me and stays in Brazil, does that change the BAH?

Is she in DEERS? That is the key to you getting any money at all.
Everyone that has given you answers is pretty close, but not exactly right. First, you ahve to have a contract for housing to get any money whatsoever. Since you are coming to Korea on a dependent restricted tour where she lives in not really important. If you were planning to move her to the US you would want to make sure the place she is going to live is in your orders. This not only helps you with moving expenses now, but it will help you with moving expenses on your follow-up assignment.
If she is going to stay put in Brazil, or she is going with you to Korea, her being on the orders is less of an issue. It used to be that if you were not command sponsored you got table rate BAH. That is not the case now. Now, no matter what your commmand says about it you will get standard OHA. Where the command comes into play is with whether or not you will get to live off post with her or whether you will need to maintain a room. Now, I am not sure what the rates are for Brazil, you will have to look that up, but I am guessing that it will be standard table rate BAH. I gave you a link below.
So much stuff in Korea, to include getting command sponsorship, depends on your command and your rank. These days there are only three major areas where having command sponsorship is helpful: driving privileges (for E6 and below), health care, and schooling for your kids. Other than that, sponsorship vs no sponsorship doesn't really matter. It does not even matter for getting your spouse a Sofa Stamp (VISA) or a ration card. We had a commander try to deny a Specialist's wife and kids both the stamp and the card by not signing memo's, but legal assisstance hooked up the commander and the troop got his stuff.
In closing, where the hell is your leadership? Why are they not squaring you away on this? Don't you have an S1 to talk to? It is pathetic that you are having to use Y!A for answers to these questions. Don't you have a sponsor? If not, feel free to email me with your AKO address. I will get you whatever info you need.

Your BAH is based on your assigned duty station location.

It depends on Rank. I was a PFC when I married my wife. (she's Korean) I got around 600 dollars more a month in pay. It was high because she had no American employment, and they can't check on Korean or foreign jobs. When I was promoted to CPL I recieved about 700. My wife wasn't even an American citizen, and had no visa for America. But we got married on base and licensed it with the American Embassy, But finance will want to see a valid American Marriage license for you to get your BAH. If you are at least an E4 you could also qualify to live offbase and have a housing allowance. If you are an E6 or over you can qualify to drive a car in Korea. If you are in the O series of rank you qualify for about everything.

If the tour is non-command sponsored, then your BAH would be based on your last duty station. If you're non-command sponsored, then most of the cost for the move is on you (her ticket, pets, POV, etc.). Also you would have a weight limit as to what you could ship over at govt expense. I'll go first and get everything set up.