Thank you for contacting me about your Tax issue. I will work hard to help you understand the issue clearly.
There are no special deductions on a tax return for "room and board" of any persons you cannot claim as a dependent on your tax return.
The exemptions of $3900 (in 2012) per person is the "tax deduction" for claiming a person as a dependent which takes this cost of feeding a person into account, effectively. So you either get the dependent exemptions, or you do not. Nothing in between.
The father cannot legally claim the children as dependents unless a court has mandated such an arrangement, or unless he either provides MORE than 50% of the costs of supporting the dependents OR he paid at least 10% of the support costs and nobody provided at least 50% of such costs and someone gave him written permission to claim his children as dependents.
So, if a court gave him permission to claim the children as dependents, then there is nothing anyone else can claim as a deduction from income.
Thank you. You answered my question.