Both 1099-MISC are for self-employment when you get down to it. The 1099-MISC income (and any other "earned" income) that the student may have, is reported on the student's tax return. It will be reported on SCH C as a part of the student's tax return.
All education stuff, regardless of who it was issued to, is reported on the parent's tax return. The student will not claim anything for education expenses at all, on the student's tax return.
In order for the student to claim anything for education, the parent can NOT claim the student as a dependent, and therefore the parent can NOT claim anything for education. Then the student's education credits are based on the students "EARNED" income.
You the parent have more earned income than the student does. So you the parent will benefit more on the education credits and deductions. So based on that, you the parent claim any and all education stuff on the parent's return.
