Having been a carer, firstly it is against the rules of any agency for careers to discuss their financial situation, it leaves the door open for accusations of seeking gifts, and in many cases that is what it is. It can be tricky, you do form friendships but this was always a big no no.
If she employs them directly, she is their employer, which means she responsible for all the statutory responsibility of any employer, checking Right To Work, tax, NI, enrolment in a pension scheme and making a contribution, she will have to retain their P45, do annual tax reporting, pay employer NI contribution, maintain the required records, have employer liability insurance pay sick and holiday pay in accordance with a contract of employment, then there could be maternity leave, long term sickness if it happened.
It’s a lot of responsibility and would cost her, as the agency introduced the career there would probably be an introduction fee to be paid to the agency. It’s not as simple as giving them cash in hand every week, which might be what they are after. That gets the employer in trouble.
The big concern is the career discussing their finances, they should not put that concern on their clients, even if the client starts the conversation. It’s not fair that your mum has been given this dilemma. Personally I would have a gentle word with the carer and ask them not to discuss their finances with your mum, or have a talk to the agency, I would worry that they are looking for financial gifts.