Yes, you qualify as an independent if you provide more than half your own support, even with unearned income*.
But, be sure that you really provide more than your half you own support**. Scholarships do not count as your own support. Loans co-signed by your parents don't count as self support. The support value of the home, provided by the grandparent, is the fair market rental value of the home plus utilities & other expenses divided by the number of occupants.
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
*You will not qualify for the refundable portion of the American Opportunity credit because your support was not with earned income, even if you qualify as a non dependent.
**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.
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.
See full dependent rules at: https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Ret...
There's a chance that you could be the QC of either your Mom or your grandparents, since you live with all three of them.
