Nominee income

You can report interest on your tax return even if you didn't receive Form 1099-INT. If you are splitting the amount with another person, enter only the portion that belongs to you.

Further, if you receive amounts that should be shared with another person or entity, you are considered a nominee recipient. You must file a Form 1099-INT with the IRS and furnish Form 1099-INT to the other person. 

You may be able to do this from the Quick Employer Forms site.

To find out the amount of interest IRS paid on the refund, subtract the amount of refund shown on your father's final tax return from the amount of the refund check.  The difference is interest.  If you still have a copy of the refund check, the amount of interest is probably on the check.

Since there is no 1099-INT, I'm assuming the amount of interest paid was less than $10.  In that case, I wouldn't worry about reporting the total amount of interest and then deduct half of it as nominee interest.  I would simply report half of the interest on your 1040 and advise your sibling that s/he also needs to do the same.

If the amount of interest is over $600, the estate may need to file a 1041 fiduciary income tax return.  As far as the IRS is concerned, the interest income probably belongs to your father's estate, not you.  But an estate doesn't generally need to file a 1041 unless it has more than $600 in income.

To answer your question on entering nominee interest deduction, you would enter the total amount of interest, then tell TurboTax you need to adjust the taxable amount under the "uncommon situations screen, then select "I received all or part of this interest for someone else (I am a nominee".   It doesn't sound like you need to do that though.