I've had some experiences with US visitors visa, was successful on two of them for my wife, and unsuccessful on two of them for step-daughter. The key to the US Embassy on visitor visa is proving that the Thai has excellent reason to return to Thailand, not stay in the US illegally. I tried everything for our then 12-year old daughter, had round-trip airline ticket, letter from school, proof we had built and lived in home in Surin, everything I could think of, and the "nice man" at the Embassy turned her down, suggesting that "if perhaps she had a job to return to". She was 12 years old, for crying out loud!
As far as the visa for the intention to live in the US (Im-1), Wildoates, it should come down to you providing that you have the ability to support her in the US, so she doesn't have to go on welfare. We were finally successful in getting a K-2 and K-3 visa approved for wife and step-daughter, but with the change in the economy we decided we would rather live in Thailand. Still have my home in the US so we could, but probably won't.
I wish you the best of luck dealing with them, it's never any fun, try to stay patient with the idiots you will talk to, and make sure you can prove you can support her.
Chok dee!