This is the K3 visa in Thailand. If you are married to a Thai national then you will need to ensure that your marriage has been registered. See marriage registration on this website. If you are not married then the K3 visa is not what you need unless you are going to get married in Thailand. Note that much like the K2 visa for children of a Thai fiancée there is also a K4 visa for the children of your Thai wife if they are not US citizens.
K3 visa in Thailand
By definition a spouse is someone who you are legally and officially married to. This means that the marriage registration with the Thai government has been completed. The traditional Thai marriage is not a legally binding marriage until such time that you have registered the marriage. Once you have obtained the K3 visa in Thailand you will need to ensure that there is also a K4 visa for any minor children. This is normally added to the initial form to show that there are children or a child being part of the process.
Important to note that polygamy is not allowed. If you are divorced then you will need to have the documents to prove this. In you have more than one wife such as under Islamic marriage in Thailand, then only the first wife may apply for and obtain a K3 spouse visa. If you have a polygamist marriage then take proper legal advice in this regard. You will note however that polygamy is not allowed in Thailand as well, however the traditional marriages which are unofficial do accept this as part of Thai culture as well as in Islamic culture in Thailand.
Filing of the Petitions
In order to start the process you will need the I-130 petition for an alien relative. Once this is done and you have received your receipt you will then also need the supporting documents for the I-129F. Note that you will first need the approved I-130 petition. Once the I-129F has been approved this documents will be sent to the US Embassy in Bangkok. The Embassy will then send you a list of other documents that will be needed and normally the lawyer in Thailand will manage all of this for you.
Once all the documents have been obtained they will then invite you for an interview at the Embassy. Note that there is also a medical examination and the US Embassy will be very specific as to where you can have this done in Thailand from a list of hospitals. Once the interview has been competed they will then issue your Thai wife the US K3 visa.
Children and the K3 Visa in Thailand
You will note that normally you will add the children to the original I-130 petition. They will also need to be added to the I-129G form to ensure that the child or children are in the process. This can make the process more difficult however they can apply for the K4 visa later if they had not been added before. Always take proper advice before you start the K3 visa process.