Does a trustee for minor beneficiaries of a will have a right to request bookkeeping records from the estate?

You don't explain any way in which those records are related to the performance of the trustee's duties. As a general matter, the trustee's rights and powers are limited to those set forth in the will, which means he cannot contest the will or the accounting of any other fiduciary. Beneficiaries, on the other hand, may generally demand an accounting.