Your mom does file it on her return, but as a "nominee". She received the money, but the 1099 forms listed someone else. If she's filling out IRS forms herself, she will probably need to find a place for "nominee interest" or "dividends as a nominee". And she'll list the social security number of the person who received the interest / dividends.
If using tax software, look for "nominee" handling. Typically I see this when the tax software is trying to input a 1099 form, and there's an additional field referring to receiving money as a nominee.