Based on what you said, they lived with you 9 months of the year, and with her 12 months of the year. That would make her the custodial parent and she would need to provide you with Form 8332 to transfer the exemption to you. Again - who paid how much in support no longer plays any role in claiming children as dependents.
However, that doesn't mean she can transfer the exemption to her brother. The ability to transfer the exemption of a child comes under the "divorced or separated parent" rule, and her brother is neither.
