Yes, split the 1099-Q into two separate ones.
Your plan administrator didn't "do you right" by doing that, but it's not technically wrong. The 1099-Q is only an informational document. That is, it is not required to be entered on your tax return. But it's needed for Turbotax to crunch the numbers.
Alternatively; you can just not report the 1099-Q, at all, if your student-beneficiary has sufficient educational expenses, including room & board (even if he lives at home) to cover the distribution. You would still have to do the math to see if there were enough expenses left over for you to claim the tuition credit. You cannot double dip! When the box 1 amount on form 1099-Q is fully covered by expenses, TurboTax will enter nothing about the 1099-Q on the actual tax forms. But, it will prepare a 1099-Q worksheet for your records, in case of an IRS inquiry.
On form 1099-Q, instructions to the recipient reads: "Nontaxable distributions from CESAs and QTPs are not required to be reported on your income tax return. You must determine the taxability of any distribution."
