Your wife has an absolute right to claim the child as a dependent.
Your wife's boyfriend can only claim your child as a dependent if,
- your wife has less than $12,400 of taxable income and either does not file a tax return, or files a return to get a refund of withholding and claims no deductions, credits or dependents.
- the child lives in the same home with the boyfriend for all 365 days of the year
- the boyfriend pays more than half the child's support. This means that whatever other support the child has (including money from its mother and your disability check) the boyfriend must pay more than all the other support added up.
Even in this case, the child would get the boyfriend a $500 tax credit, not the $2000 credit, and does not qualify the boyfriend to claim EIC.
