It may be possible to claim a dependency exemption for a relative living in Mexico. While the niece cannot be a qualifying child because she does not live with you, the niece may be a qualifying relative. As long as she cannot be claimed as someone else’s dependent, then you can claim a dependency exemption (assuming all other dependency exemption requirements are met).
A tax triggered if certain tax benefits reduce your regular income tax below the tax computed on Form 6251 for AMT purposes.