What can I say or do to have primary caregiver see that she is experiencing burnout?

Wow. I can so identify. I am the one who "can do it RIGHT; the ONLY one who can do it right" and have, in times of great stress, asked for help, wailed for help, then found myself standing there and critiquing the help; this isn't right and that isn't right, and fold it this way, not that, and "Oh, I had better just do it myself". I learned a great lesson with what I do. It just took me 78 years to learn it. I so identify with your Mom.
I would say sit her down, say that you and bro are doing what you can, and wish it was more, but realize your own limitations for your own lives. Tell her you are worried about her. Tell her that her being so capable can be her own worst enemy. You know now that strokes can happen in your family and can happen early. Encourage your Mom to talk with you; ask her what is the worst thing for her now. Ask her if she recognizes that Mom cannot remain alone forever and that the need for placement WILL come; that it were best Mom is still alive then to be Grandma's support in loving visits and managing what she can for her. This is the first year.
Try not to be what you see Mom attempting, a "Ms. Fix it". This can't be fixed. This has no good answer. Mom will start to use the "guilt" word when she understands she cannot go on. You need to let her know she is not an evil felon but a daughter with limitations, and with great grief that she is not a Saint. Grief understands not everything can be fixed. Guilt assumes there is an answer. And really, there IS no good answer.
Just try to help Mom understand human limitations; tell her that he ability to do so much for so many and do it RIGHT is leading herself and others to think her abilities are limitless and can go on forever.
This is all full of grief. It is WORTH MOURNING. Your Mom will have times she needs to just break down and weep. Give her little surprises. A Casserole, a take out dinner, a bottle of WINE (but not too many), a book on tape, flowers and most of all a note saying she is like the best thing ever, but you are scared for her. Just as you told US.
So sorry. What a good daughter you are. I have a couple, as well. Pat yourself on the back for your loving heart, and understand, just as Mom can't fix this all, either can you.

If the reasons mom does not want to hire another caregiver because of the involvement of making sure they show up on time (or at all) and paying them on time why not suggest that 2 or 3 days a week the caregiver she does have extend her hours. 1 or 2 extra hours might make a big difference.
So rather than them working only when mom is teaching have them stay an hour or two longer.
Also make sure that the caregivers are doing what they should be doing and suggest to mom that she add another task to their schedule.
Clean bathroom, do laundry.
with the extra hour or tow that they are going to work maybe one day they can do shopping. Mom can order on line and they can go pick up the order. (that way caregivers are not going to be having to pay for the items)
One of the "problems" might be your mom's mind set. A lot of caregivers think "no one can take care of XXX the way I do". They won't do the laundry the way I want it done, they won't make dinner the way I do it. They won't do whatever..the way I do it. And no they won't, no one will do it the exact way you do things but if the job gets done it is one less thing you have to do. But it is giving up some bit of control. And it is change. As humans we WANT / NEED to be in control and we HATE change.
next time you see your mom just give her a big hug!

I think it is a matter of balance, if your mom feels she needs to continue to control these extra duties for your Grandma then she needs to let go of some of her other obligations - perhaps a cleaning service for her own house, more prepared meals and less home cooking, and her husband needs to step in to make sure everything else on the home front is taken care of because that's what partners do. And figuring out a way to include a block of respite time for her every week (time where she isn't obligated to do anything or be any where, every Sunday morning for instance) can be a huge benefit.

You have a good heart to care not only for your grandmother but also for your mother. I agree your mom is experiencing burnout, and she probably recognizes it as well. Your mom has a need to fill this role and not allow more help. Try asking your mom why she feels she must always be the caregiver. Ask her what her fears are about allowing others to help more. You may not get her to agree to more help, but you will understand what motivates your mom in her role as caregiver.

In my experience, my mom cared for my grandmother exclusively for 7 years with very little outside help from family. She left her job and "Gram paid mom" out of her family trust at minimum wage and for part time hours. I tried to explain to my mom that caregiving needed to be balanced self care: time off to be with friends without Gram, time for her own hobbies... Mom said she did her own hobbies at home and saw friends once a month. It took my mom 2 years after my grandmother passed for my mom to get her own life together: having to sell her home because she didn't have the finances to keep it, selling most of her belongings to downsize to a small condo, and buying most of her stuff now at thrift stores and discount places.

As a family member maybe you can support your mom by contributing to your Grandmas care. Maybe sit down with your mom and draw up a list of duties you can do to help her out.
I can well understand that your mom resists outside help. It’s hard to get good consistent reliable help. I know as I’m caregiver to both my parents. The best gift my siblings can give me is to make meals once in awhile for my parents. After all they are their parents too. I cook, clean, look after meds etc. When I finally took a break I came home to having to clean. Sibling in charge then just didn’t see the work.

It's great to show your mother support and help, but, if she continues to resist reasonable measures for support that actually would HELP your grandmother, I'd have trouble tolerating it. She's rather young to be lacking in good judgment. Do you think she'll change her mind if you persist? She may be slow to delegate, but, sometimes, you have to do that in order to protect the safety and welfare of a senior. IMO, some people have to do it all for different reasons. Some are martyrs, some are control freaks and others can't afford outside help. If there are funds available to get the help, I'd figure a way to make it happen. Who is POA?

I was that caregiver. I don’t know what you can say to make a difference. I had to figure it out on my own to some extent.

I was listening to others but it took me being sick and tired of being sick and tired.

outofservice: Thank you for reaching out and being proactive instead of reactive about your mother in her caregiving role to your grandma. Even though your mother is quite young, she could burn out. Encourage her as best you can to seek respite. Prayers sent.

To update:
Mom was able to sustain, in my opinion, the impossible for a while longer. When Mom had time during the holiday vacation, she pursued a caretaker for the weekend. Since the New Year, the Weekend Caretaker is performing well and Mom appears less stressed.