Yes, your daughter has $1600 of taxable income.
I'm not sure why you selected $2000 as the alternate amount for the AOTC. The amount to report is $3600 (1600 + 2000) for a $2000 AOTC or $5600 (1600 + 4000) for the max $2500 AOTC.
You should go for the max, as your daughter should owe no tax, considering her $3000 other income.
This is not some sinister scheme. From the 2018 form 1040 instructions (pg 100): “You may be able to increase an education credit if the student chooses to include all or part of a Pell grant or certain other scholarships or fellowships in income. For more information, see Pub. 970, the instructions for Form 1040, line 17c, and IRS.gov/EdCredit".
