Simple answer: No.
The reasons are not so simple.
There are two types of dependents, "Qualifying
Children"(QC) and standard ("Qualifying Relative" in IRS
parlance even though they don't have to actually be related). There is no
income limit for a QC but there is an age limit, a relationship test and
residence test. Only a QC qualifies a taxpayer for the Earned Income Credit (EIC)
and the Child Tax Credit (CTC). They are interrelated but the rules are
different for each.
Because you brother and his niece do not live in the same
household; she cannot be his QC. She might still qualify as his qualifying
relative, if he provided more than half her support*. But, he could only claim
her exemption for a $4050 deduction. He could not claim her for the EIC or CTC.
Your daughter can be your QC or she can be your grandmother’s
QC. Either of you will, most likely, get a bigger refund than your brother.
*From what you describe, it is unlikely your brother meets
the support test, since your grandmother is furnishing housing. If no one person provides 50% of the support (in your case, 3 people are providing some support), then a "multiple support agreement” (IRS Form 2120) can be used,
to allow one to claim the dependent. https://www.irs.gov/pub/irs-pdf/f2120.pdf
The IRS has a worksheet that
can be used to help with the support calculation. See: http://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf The support
value of a home is the fair market rental value, divided by the number of
occupants.
