If the horse is papered in her name, you will have to send AQHA a copy of either the Letters of Administration or Letters Testamentary, then the Administrator or Personal Representative of her estate can fill out the transfer to you.
If your mother's estate was not probated, you will need to file an Affidavit of Heirship (available only by calling AQHA).
Those would be the only correct ways to do it. The filing fees are the same no matter how you do it, but the extra paperwork can be a pain.
*some shady people* will falsify transfers for a date before person died to avoid the paperwork hassle. This probably would go completely unnoticed if the horse will never be shown, but it is definitely NOT RIGHT.