Without the ability to look at your tax information on this public tax forum, I can only provide possible solutions to your tax questions.

On reason is that as a dependent, her standard deduction is different than other taxpayers and she doesn't have an exemption deduction.

From the IRS Topic No. 551 Standard Deduction

Dependents -  If you can be claimed as a dependent by another taxpayer, your standard deduction for 2017 is limited to the greater of: (1) $1,050, or (2) your earned income plus $350 (but the total can't be more than the basic standard deduction for your filing status).

It is quite likely that she is only getting a standard deduction of 1,050 dollars in this case. This 1099-G for the grant is most likely not considered earned income.