Room & Board are allowable expenses for a 529 Distribution. You may use your actual cost or the school's ''allowance for attendance", which ever is lower. My local state college has an allowance of $11,500/year. Assuming her school is as little as 75% of that, the 529 distribution is tax free to you. She does not need to claim the full $10,000 tuition to get the maximum LLC (In her case only about $1500, because of her income).
For simplicity, just don't enter the 1099-Q on your return. You know none of it is taxable.
On her return, she enters the 1098-T, exactly as received. She does not need to make any adjustments for what you claim because there is already enough "left over", for her return.
