Q. What if the 1098-T is my child's name?
A. It does not matter. It also does not matter if the 1098-E is in the student' name
As long as the student is the beneficiary of the 529 plan, you may use the 529 distribution to pay off the student loan, including interest and principal. If you paid the interest with 529 money, you may not also claim the student interest deduction. That would be "double dipping" on tax breaks.
As to the 2nd loan, you may only, claim the interest deduction if you are legally obligated to pay it (as well as you actually paid it). That is, the loan must be in your name or you co-signed for it. It does not matter that the 1098-E is in the student's name. One additional requirement: the student must have been your dependent at the time the student loans were used to pay expenses.
