You may claim them as dependents if the following conditions are met:
In your circumstances, the mother can not be required to file a return, nor can she claim her child or herself on any return.
So the botXXXXX XXXXXne is....yes.
Refference IRS Publication 501 AND
IRS notice 2008-5. http://www.irs.gov/irb/2008-02_IRB/ar14.html