Dependents

maybe not. however, the tax laws determine who can claim a dependent. in any one year, there is only one person that qualifies to do that.  the laws don't require that person actually do so but that does not give any other person the right to claim them.

generally, that person is the custodial parent who can claim them as a qualifying child.  Your brother wouldn't be allowed to legally claim them - they d be deemed a "qualifying relative" because a parent wh can claim as a qualifying child has a higher priority.

@cbjackson414  said "I was going to allow my brother to claim my kids as dependents but he got a letter stating he didn't get the child credit".

That sounds like your brother actually claimed the children.  He will now have to file an amended return to unclaim them.   In the meantime, the IRS will process your return.  That is, it was not necessary for him to have first filed his amended return.  

But, as to the issue of your brother being allowed the child tax credit, for your kids; that depends on whether he lives with you (or you live with him).

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, student status, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. They are interrelated but the rules are different for each.

The support test is different for each type. The support test, for a QC, is only that the child didn't provide more than half his own support. The support test for a Qualifying Relative is that the taxpayer provided more than half the relative's support.

.A child closely related (an uncle counts) to a taxpayer can be a “Qualifying Child (QC)” dependent, regardless of the child's income, if:

1. He is under age 19, or under 24 if a full time student for at least 5 months of the year, or  is totally & permanently disabled
2. He did not provide more than 1/2 his own support
3. He lived with the relative (including temporary absences) for more than half the year
4. He is younger than the relative (not applicable for a disabled child)
5. If the child meets the rules to be a qualifying child of more than one person, your brother must be the person entitled to claim the child as a qualifying child (this essentially means that he must have the your permission to claim the child, if the child also lived with  you for more than half the year)
6. If the parents of a child can claim the child as a qualifying child but no parent so claims the child, no one else can claim the child as a qualifying child unless that person's adjusted gross income (AGI) is higher than the highest AGI of any of the child's parents who can claim the child.

See full dependent rules at: https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Return/INF12139.html