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The support test for a “qualifying child” (QC) dependent is only that he didn’t provide more than half his own support. So, it also doesn't matter if the 20yo doesn't provide more than half his sibling's support. But there are special rules for divorced parents. But to be applicable, the two parents together must have provided more than half the child's support. So, it does matter how much support you provided.
So, the 15yo is the qualifying child of his 20yo brother. I'm of the opinion that the IRS will honor your signed form 8332, because you are the parent and he is only a sibling (tie breaker rules).
But, your older son’s claim of his younger brother as his QC dependent will trigger an IRS audit, if you both claim the child. One of you will have to pay back all (or most) of his refund.
The smart thing for the older brother to do is only claim his younger brother for EIC and not CTC or dependency. That is allowed.
HOH, for the 20yo, is another whole issue, but you, as non-custodial parent can NOT claim HOH, on your return, based on the 15yo dependent, regardless of what the 20yo does.
