How do I enter higher educational expenses for a non-dependent child so I won't pay taxes on his 529 distribution payment? (from my 1099-Q)

Since you know that the distribution was fully covered by expenses, just don't enter the 1099-Q.  The 1099-Q is only an informational document. The numbers on it are not required to be entered onto your tax return.  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. You would still have to do the math to see if there were enough expenses left over for the parent to claim the tuition credit. You also cannot count expenses that were paid by tax free scholarships. The family cannot double dip!  

Otherwise, In TurboTax (TT), enter at:

Federal Taxes Tab (Personal for H&B version)

Deductions & Credits

-Scroll down to:

--Education

  --ESA and 529 Qualified Tuition Programs (1099-Q)

You will be asked who is the student; answer "Someone else not listed here".  You will eventually get a screen "Non-dependent Student expenses" to enter the expenses.

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Qualified Tuition Plans  (QTP 529 Plans) Distributions

General Discussion

It’s complicated.

For 529 plans, there is an “owner” (usually the parent, but can be someone else, like grandparent), and a “beneficiary” (usually the student dependent). The "recipient" of the distribution can be either the owner or the beneficiary depending on who the money was sent to. When the money goes directly from the Qualified Tuition Plan (QTP) to the school, the student is the "recipient". The distribution will be reported on IRS form 1099-Q. 
The 1099-Q gets reported on the recipient's return.** The recipient's name & SS# will be on the 1099-Q.
Even though the 1099-Q is going on the student's return, the 1098-T should go on the parent's return, so they can claim the education credit. They can do this because the student is their dependent.

They can and should claim the tuition credit before you claim the 529 plan earnings exclusion. The educational expenses you claim for the 1099-Q should be reduced by the amount of educational expenses they claim for the credit.
But be aware, you can not double dip. They cannot count the same tuition money, for the tuition credit,  that gets you an exclusion from the taxability of the earnings (interest) on the 529 plan. Since the credit is more generous; use as much of the tuition as is needed for the credit and the rest for the interest exclusion. 

 In addition, there is another rule that says the 10% penalty is waived if you are unable to cover the 529 plan withdrawal with educational expenses either because he got scholarships or the expenses were used (by him or the parents) to claim the credits. 

Total qualified expenses (including room & board) less amounts paid by scholarship less amounts used to claim the Tuition credit equals the amount you can use to claim the earnings exclusion on the 1099-Q. 
Example:
  $10,000 in educational expenses(including room & board)

   -$3000 paid by tax free scholarship***

   -$4000 used to claim the American Opportunity credit

 =$3000 Can be used against the 1099-Q ( on your return)

Box 1 of the 1099-Q is $5000

Box 2 is $2800

3000/5000=60% of the earnings are tax free; 40% are taxable

40% x 2800= $1120

You have $1120 of taxable income  

**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. Again, 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." 

***Another alternative is have the student report some of his scholarship as taxable income, to free up some expenses for the 1099-Q and/or tuition credit. Most people come out better having the scholarship taxable before the 529 earnings.