your wife must have been given parental authority by the court when her marriage was annulled ?
did the embassy interview the kids ?
if i was you i would appeal like Iain has said,
and provide evidence your wife has custody of the kids.
provide evidence of where their father is, so they can contact him. - did the father mention he doesn't support them financially or has little or no say in their upbringing ?
evidence of 'sole responsibilty' -
http://www.gherson.com/News/Sole-Res...in-the-UK.aspx
does your wife have school bills?, a letter from the principal of their school stating your wife is the one who pays the bills, attends parents evenings etc,
medical bills for them ? evidence that your wife provides for them financially and is responsible for their upbringing..
i'm sure if you can get this evidence your app could be reconsidered, if not as Iain has said, i think to, you would win an appeal, but you dont want to wait upto 8 months without her kids.
seek some expert advice to from your local law centre, cab, or
http://www.iasuk.org/home.aspx