There have recently been some changes in Kyiv for children under 16 to obtain immigrant or non immigrant visas.

http://www.usemb.kiev.ua/visa_nonimmigrantvisas_eng.html

From the embassy web site.

Children under 16 do not need to come in person unless the child is applying for a student visa to the USA.
***However, in ALL cases involving children under 16, both parents must be present with their passports and the child's birth certificate for the child to be considered for a visa. There are only three exceptions to this rule. They are: 1) One or both parents are in the U.S. and evidence of this is available. A parent present in the U.S. must also provide a notarized power of attorney from a U.S. notary giving permission for the child to travel to the U.S.; 2) One or both parents are deceased and evidence of this is available; or 3) One or both parents have been denied parental rights to the child and evidence of this is available.***