Children of your fiancé will require their own visa to enter the United States.
When you apply for your fiancé using FORM I-129F, you must list any children of your fiancé on that form in Part B, question 13. Failure to list the children on this form will prevent them from obtaining a derivative visa with your fiancé.
At the time of your interview, you must provide the child’s birth certificate, legalized as your fiancé’s; you must also fill out FORM DS-156 for each child.
Per Dominican law, a child must also obtain “Permission to travel” this is a document that must be drawn up by a Dominican Lawyer; it is brought before a local judge and legalized by the court system in the Dominican Republic.
When you apply for your Fiances K1 visa and list the children on Part B, question 13, they will be eligable for derivative status, this means that they may accompany your fiance and will be given a K2 visa.
You should note that both the K1 and K2 visa's have significant restrictions, for more information visit:
http://www.dominicanstotheusa.com
Q: What is a K2?
A: A K2 visa is a derivative visa of a K1; this means that if you have applied for a K1 fiance visa, any children of your fiance may accompany them to the US under a derivative status, you must however apply for their Permanent Residency when you Adjust Status of your Fiance.
http://dominicanstotheusa.com/forum/index.php/topic,2262.0.html
CHILDREN ACCOMPANYING YOUR FIANCÉ