It sounds like your client's mother needs a caregiver of her own. She is not your client and has no business hounding you. This is attention-seeking behavior. You've handled it as nicely as you could, but now you have to get firm and stern. When you set a boundary, remember you also have to abide by it. That means ignore her texts. She has absolutely no business calling you when you are not on duty with her daughter. Even then, there is a limit to how much interaction there should be between the mother and you. If the authorities have decided that the daughter can live on her own, with caregiver support, then the mother should back off. When you're off-duty, the mother should only call the agency.

I've done homecare. By rights, if you're not needed, the client, or her mother, should call the agency. Then the agency should call you. Sometimes, it's best to not give the client or family your phone number. You were trying to be nice and accommodating, but this mother takes advantage. It's very unfair for them to cancel you at the last minute, making you lose a day's pay. An agency can refuse service to someone who does that repeatedly. Unfortunately, these agencies don't care about you losing pay. They just care about having as many clients as they can make money off of. Some agencies do pay caregivers something, if they get canceled at the last minute. Sounds like yours doesn't. So they see the cancelation as no skin off their nose.

You have to establish some expectations with this agency. I'ld recommend not giving your phone # to any clients or families. Tell future clients/families that they can only get a message to you by calling the agency and talking to them, whether it be a cancelation or whatever. Your supervisor gave you some good advice, but did not go far enough. The supervisors should be telling clients/families that all cancellations have to go thru the agency. The supervisor is shirking responsibility by acting like this is just your problem.