How do I claim the $4000.00 to get the $2500.00 tax deduction if my Father used the 529 plan for Samantha he has to pay the balance after loans and grants?

If you have a 1098-T, and you should, enter that form. Box 1 should report what was paid to the school for the entire 2020 tax year. 

If part of that amount was paid for with 529 funds, report that 529 amount as additional scholarship in the TurboTax program so that the program can do the math. 

The 1099-Q (distribution form 529) should be issued to the student, but might be send to your father. As long as it was used for education expenses, and you don't use those same expenses towards the credit, the 1099-Q needed be reported on anyone's tax return. It will be informational only, although it would be good to keep a record of the expenses and who claimed what in case the IRS ever inquired. 

According to the IRS:

“The American opportunity or lifetime learning credit can be claimed in the same year the beneficiary takes a tax-free distribution from a Coverdell ESA, as long as the same expenses aren't used for both benefits. This means the beneficiary must reduce qualified higher education expenses by tax-free educational assistance, and then further reduce them by any expenses taken into account in determining an American opportunity or lifetime learning credit.”

IRS Pub 970

If box 1 of the 1098-T is at least $4000 more than box 5, you enter the1098-T on your tax return and enter no other numbers.  Do not  report the 529 amount as additional scholarship in the TurboTax (TT) program.   

TT will use $4000 to calculate the $2500 credit for you.  This assumes you claim Samantha as a dependent on your return.

You tell your father (or Samantha if she is the "recipient" of the 1099-Q) to reduce the amount of tuition expense that they claim by $4000.

Your part is that simple.  Theirs is more complicated, See below

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Qualified Tuition Plans  (QTP 529 Plans)

It’s complicated.

For 529 plans, there is an “owner” (usually the parent, but apparently the grandparent in this case ), and a “beneficiary” ( the student ).  The beneficiary does not have to be the owner's tax 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 you can claim the education credit. You can do this because he is your dependent.

You can and should claim the tuition credit before claiming the 529 plan earnings exclusion. The educational expenses he claims for the 1099-Q should be reduced by the amount of educational expenses you claim for the credit.
But be aware, you can not double dip. You cannot count the same tuition money, for the tuition credit,  that gets him 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. Another special rule allows you to claim the tuition credit even though it was "his" money that paid the tuition.
In addition, there is another rule that says the 10% penalty is waived if he was 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. He'll have to pay tax on the earnings, at his lower tax rate (subject to the “kiddie tax”), but not the penalty.

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 (usually on the student’s return)

Box 1 of the 1099-Q is $5000

Box 2 is $600

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

60%x600= $360

You have $240 of taxable income (600-360)

**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.