My mom is 89 and lives by herself. she is in need of some assistance on a daily basis as far as meal preparation, med reminders and errands. she has hired a CNA that wants to be paid cash ($15/hour). I am trying to convince her that she needs to be going through a service to get all the benefits and resources her money can buy. She will not listen to reason and doesn't see anything wrong with paying this woman cash under the table.
If she really likes this CNA and is getting good care, perhaps it would be more fruitful to ensure that this is treated in a business-like manner. You can hire an independent caregiver, but make sure the appropriate steps are taken regarding taxes and liability.
The agency we used never had a substitute carer to fill in when our was out. Perhaps a very huge agency would, but most don't have staff sitting around waiting for a call to fill in on short notice. So I'm not so impressed with that benefit.
Agencies do screen the applicants. Some do some training; many do not.
Keep in mind that if you are paying $20/hr to an agency, the worker is probably getting about $10/hour. There is sometimes something to be said for working with a higher-paid person who has more (perhaps) vested in pleasing the client.
I am not suggesting that you DON'T try to talk Mom into going through an agency. But if you can't convince her, I think your best bet is to make the current situation legal and above-board.
My boss ran into that problem... he didn't want to pay through an Agency any more... but when his Caregiver's children were home sick from school, he was in a fix and he had to stay home himself to care for his wife... he was not a happy camper. At least when he was with an Agency, even the owner of the Agency herself came to fill in when one of her employees couldn't work that day.