Are the carers from the same agency/company or are they local authority/nhs style carers? Before jumping the gun, it might be worth doing a bit more research first. I wouldn't be putting notes anywhere - as if anyone is taking money, it'll make them stop for a while, but when the heat's died down they may start again. If the carer is stealing money, you can bet your mum isn't the only victim. I'd rather work out who did it, and take my evidence to the Police, and let them deal with it. You might be able to involve the Police of course once you have a clearer picture of what's happening. Of course your instinct is to go running in saying 'right one of you is at it - stop it and leave' - but that might cause significant short term friction without proof.
Do you live in the area of your mum's house? Do the carers follow a set schedule? First between 9-10am? Second 2-3pm? Third 5-6pm? Or something like that? Is it always the same carer at a particular time slot? Or do they vary through the day?
If you were living close by, I might check the contents of the purse last thing in an evening after the last carer visit, and then pop in again after the first visit of the day, telling your mum you just had to pop in and check something - then leave again, and do the same for the 2nd visit, and the 3rd visit. Then you can narrow down when the money has gone. If you're then able to identify which carer it is, you could then approach the Police with the evidence you've discovered, and they might suggest how you best pursue it - either potentially with a camera, or using some kind of marked notes.
I remember a few years ago I had someone stealing pound coins from the change supply in a retail stores safe. I counted all the coins first thing in the morning, and then made sure that the top few bags contained pound coins that I'd manually scratched an X into. I then checked the coins at various points through the day, and sure enough three of the bags had lost coins by midday. (Lunchtime approaching) We conducted a staff search on all present, although we knew it had to be a key holder with safe access, and there out of the pocket came £8 of crossed coins. We then took that person to one side, opened the safe, retrieved the other marked bags showing they were missing £8 - and that they were all crossed - and got an instant confession. We then followed this with the correct disciplinary route of interviews/suspension/dismissal of course.
You might be able to work with the care provider to establish theft in a similar manner. Once you've been able to narrow it down as to who is most likely, you could record the serial numbers of all the bank notes in her purse, and then in liaison with the care company, they can conduct a search once the carer has left your mum's house. If any of the notes with the relevant serial numbers are found in her possession, then you have a case for her removal, and potentially criminal proceedings. The carer may claim that the money was given to her - so that can make things a bit complicated if you don't have camera evidence.
I might consider something like this:
https://www.amazon.co.uk/dp/B087WV2LG9/ref=cm_sw_em_r_mt_dp_U_v4P7Eb62VBJHC
It looks like a clock, has it's own built in battery, you can set it up in your house where you have wifi - then plug in the SD card - and take it to your mums. It needs wifi to access it remotely, but will also happily sit there recording onto the SD card without a connection, reading through the questions and answers shows it only needs wifi if you want to remotely access - it will work as a standalone recorder once it's been initially set up. You can go retrieve the card once you identify missing money, and you might then be able to work out who the culprit was, and whether they just took the money - or coerced your mum into handing it over. For the sake of £65(plus a memory card) - this could be a good long term investment for any future carers. (you don't even have to tell your mum it's a camera - just tell her you were presented the clock for your 10 year service at work or something - and you'd love to see it in her living room whenever you visit - make her proud to want to have it there!)
