When it comes to educational tax credits and deductions, the first place I go to is IRS publication 970 () . Let me assume your daughter is an undergraduate within her first four years of college and that she doesn't provide more than half of her support, the most common situation, and therefore you can and do claim her as a dependent. Looking at page 20 of Publication 970, you can claim the American Opportunity Credit (AOC) for her qualified educational expenses (tuition, books, but not room and board per page 13) that you or your daughter pay out of pocket, i.e. not covered by scholarships or prepaid/529 plans. Only the first $4,000 of such out of pocket expense qualify for the credit. Continuing on page 20, if your mother had paid the money directly to the college for tuition, it would count as your daughter's contribution which is simply lumped back with your as qualified expenses eligible for the credit.
Because your mother gave you the money, it was you that paid for college expenses and the AOC would still be claimed by you. Your mother's contribution is considered a gift to you. If that gift was no more than $15,000 there is nothing to be done. If it was more, you mother might of said or implied it was given to you and your daughter and, if available, your spouse. That would boost the exclusion by a factor of 2 or 3. Beyond that, your mother would need to keep track of the excess amounts which would potentially subject her estate to a gift tax. The good news is that unless such excesses total well over $11,000,000 there would not be any gift tax after all.
Finally, money paid directly to the college by your mother (or anyone else) on your daughter's behalf, is not considered a gift at all. Ditto for medical expenses paid to a medical institution.
