I assume that the Form 1099-R that you received has code 4 in box 7. Unfortunately, an IRA inherited by a non-spouse beneficiary is only permitted to moved from one inherited IRA to another by nonreportable trustee-to-trustee transfer (which you attempted to get the old IRA custodian to do). Distribution and rollover is not permitted. This means that the entire distribution is taxable and the deposit into the new inherited IRA constitutes an excess contribution. The CPA you talked to should have known this. Because TurboTax knows that a code-4 Form 1099-R issued to a non-spouse beneficiary represents a distribution that is not eligible for rollover, TurboTax will not permit you to report the distribution as having been rolled over.
Had the check been made out to the receiving IRA, not to you personally, and the check was given to you simply to convey the check to the new custodian, this would have constituted a nonreportable trustee-to-trustee transfer, but in that case there would have been no tax withholding. The fact that taxes were withheld seems to imply that there was indeed a distribution from the original inherited IRA.
Congress has been discussing changing the tax code to permit rollovers of inherited IRAs by non-spouse beneficiaries, but that change hasn't happened.
(The only type of distribution and rollover permitted by a non-spouse beneficiary is a direct rollover from an employer plan like a 401(k) to an IRA, reported with codes 4 and G or 4 and H in box 7 of the Form 1099-R.)
