I want to ask for a raise... Should I ask for an increase in pay to match what she pays the agency caregivers?

I would bet that the agency caregiver is earning about ½ - ¾ of the amount being paid to the agency. The agency has all sorts of additional costs the need to recoup in their fee. They have to also cover their overhead for their office and staff and now that they will need to track the employee location and hours via Electronic Visit Verification they have a huge expense putting and maintaining that program. Not to mention the required annual training that the employee needs to go through. They need to pay the employee for those hours and also pay other staff or an outside contractor to do the training.

Keep in mind the caregiver from an agency does not get all of what is paid to the agency. There are "administrative fees" that are charged and are included with the fee the agency gets.
You can ask for an increase but do not cite the agency caregiver. Salary should always be confidential.
Do a bit of research as to what a professional with your experience and if you have any certifications.
4 years ago when I hired privately I paid 2 caregivers that had just completed a CNA certification program, they were waiting for Nursing School to start, I paid them $20.00 per hour. Taxes were taken out and their income reported.

I wish all caregivers were paid more. It’s a tough job and you certainly deserve more pay. Go ahead and ask for it.

Yes. Most certainly your pay should be at least equal to what the night shift agency workers are getting. There is no question about that. In fact, your pay should be more because you're the primary daytime CNA which means you do more and are responsible for more. Please explain this to your employer. Then tell them that it would be fair for your pay to be 4 dollars an hour more than you are currently getting. I had to talk to the family I was employed by for several years about paying me more. When I started the pay was $17.50 an hour. As the client's dementia and other conditions worsened and she became invalid, her husband became ill also and needed a lot of care. I took care of both of them. I met with the family and wrote the figure of $22 an hour on a piece of paper. That was the pay I would accept. Of course it shocked them because they couldn't believe anyone could be worth that much for this work. So, I told them either you pay it or I'm leaving now and not coming back. Of course they tried a bit of guilt-tripping about how much their parents loved and needed me and couldn't afford to pay more. It fell on deaf ears because I knew the game they were playing at. They all play at that. They paid it. I brought my own girls in on the job when they needed to hire additional help and hours. None of the others made anywhere near what I did, because they were only a couple hours companionship and the rest of the time was sleep-pay just to be there.
If you've been there for a while and they like you, they will pay it. Or at least equal to what they're paying the agency.

Lunasusu, Caregiving Agencies have a lot of overhead cost. Such as rent for their commercial office. Utilities. Business licenses. Liability insurance. Workman comp for their employees. Classes. And much more.

My Dad used an Agency for all 3-shifts, and what I liked was the fact that if a caregiver wasn't able to make his/her shifts, the Agency was able to find a replacement. The 3rd shift was required to remain awake for the whole shift, and be ready to help my Dad if he woke up and needed to use the bathroom. My Dad was paying $30/hour for every shift hour.

When it comes to pay and raises, that should be discussed at the signing of the employment contract. Yes, you probably are worth a lot more than you are getting paid. Oh, does your employer have workman comp for you should you become injured on the job, or at least an "umbrella" insurance policy?

The agency gets the money, the aides get considerably less - so don't use that as a barometer.. Also, if you're being paid off the books, please take that into consideration - no taxes being taken out of your pay. It doesn't hurt to ask for a raise but dont expect a $3.00 raise and be willing to accept what they offer.

I vote yes. If she doesn't wish to pay it you have more time of your own and she can hire another caregiver to give her less care.

You can always ask for a raise. I have done that in my job citing my accomplishments. The worst your employers can say is no.

The agency may get more $3 more but the employees get much less. If agency charging $20 an hour their employees are lucky if they get $10.

I am surprised that an agency is hiring people with no CNA or HHA certification. I would bring to the families attention that these "aides" seem to lack the skills needed to care for your client. But you needing a raise? Not saying u don't deserve it but you can't base it on what an Agency charges. You can base it on what an agency would pay an employee with ur experience.

how is your mom doing financially? i mean it is your mom i have been caring for my mother in law not getting any money. but i do live in the basement apt. for very cheap. she doesnt have much money left tho she owns 2 houses outright but the money is near gone. her daughter found out that mom left the upstate house to my husband instead of her kids and lost it. she has POA so she bought the house rather than see it go to her brother when her mom dies. she bought it for far less than it was worth. and got it full of furniture and big tractors etc...... a catskill house 33 acres for 200k i figure it was worth 243 w/nothing in it. so she ripped her mom off and messed my son out of his inheritance

When you say, privately, are you a W-2 employee or do you have a business license and have other clients?

In my state, due to Covid, W-2 Caregivers were given a $2 mandatory pay increase as Hazard Pay during Covid. Did your state do the same?

If you are a W2 employee, you could ask for a yearly employment evaluation and bring up the subject during that. If you own a business, what does your contract say about yearly price increases?

The agency is getting the money but their employees probably are getting the same -- or less -- than you. You should "shop around" to see what other private hires with your qualifications and experience are being offered. If it's more than what you are making, then yes you should ask for a raise but there's no guarantee they'll agree to it.