What do you mean "recipient?" Do you mean you were the custodian or guardian or conservator? for your mother?
Be careful with taking custodial money and putting it into a joint account. That probably not a good idea. Ask your attorney if that is permitted. Why? Because if your name is on the account personally and not as a custodian, the account is likely an asset of yours and your creditors could get it. usually you need to keep such assets out of your name unless you are giving the to the protected person. (E.g. UGMA/UTMA accounts go the a kid when they turn 18.)
Who's money is it? You're or hers?
Who gets the 1099 doesn't have anything to do with who should report it. Yes, the person who gets it must report it (or the IRS computers won't be happy), but if they are merely a "nominee" they should subtract the other person(s) share and the other person should report that share on their returns.
See this previous answers about the details of TT and nominee distributions.
https://ttlc.intuit.com/community/taxes/discussion/how-to-report-nominee-income/00/566274
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