Adjustment of status comes at the end of the visa process. Once the Thai children enter the United States using the US K2 or K4 visa. They may file for the adjustment of their status into permanent residency. With the filing of the I-130 petition on their behalf by the US national.
Your Thai wife who has obtained permanent residency can also file the petition. This if the US national failed to do so, and the Thai child should wait for an available visa number. Therefore, the best option is for the US national to file the I-130 petition.
This is so because the Thai wife already has obtained legal permanent residency in the United States, and the derivative status of the US K2 or K4 visas have ceased to take effect. Thus, the legal status of the Thai children will become terminated, and they will be considered as illegally staying in the United States and may have the possibility to face deportation.
Also, adoption of the Thai child or children is another available option for the Thai-American couple. However, the process for adoption can be complicated and takes a long period of time with the requirements for adoption by the US State Department quite difficult to fulfill, having a requirement that the child must have lived together with the adoptive parents for a minimum period of two years.
The child should also be unmarried and below 21 years old. Should the child have been adopted prior to the child turning 16. Making adoption a very tough option. It is highly recommended that the child be brought to the United States on a derivative US K-2 or K-4 visa, then file for adoption in Thailand after entering the United States.
Always take legal advice from an immigration lawyer in Thailand for legal help and guidance.