How to pay for a caregiver?

Since dementia is a progressive disease she will eventually not be able to be left alone at all. So, since you know this is coming why not start researching facilities local to you? Even if this isn't your plan right now it may need to be in the future. There may be waiting lists, as there often are, for Medicaid beds. If her name comes up and you're not ready to transition her (if this becomes your plan) then you are not obligated to accept the spot. But you do need to understand that the better facilities can have waiting lists.

My MIL (88, in LTC) is in a faith-based facility on Medicaid. She is getting great care even though this place is at least 30-years old and not "shiny and new" like other places. She isn't the same faith and they don't require it. This organization sees eldercare as a mission, so the people there don't see their work as a job. Please consider these types of care facilities for your mom. Also please consider that in-home care by family is great but LOs with dementia often are not getting much social interaction and exposure. My MIL goes on field trips, attends in-house events, clubs. church, musical events, pet visits, etc. She would never be getting much of that in my home. Of course it all depends on what's available where you live and researching takes time. You don't want to have to make a decision in the midst of a crisis, so just start looking a little every week. I wish you all the best and peace in your heart on this journey.

Get her approved for long term care Medicaid, and place her in a nursing home. Seek out and visit your local Agency on Aging, they will assist you in this process. Do not quit your job. If you have trouble placing her in a NH on your own, get help from a state social worker, you can do this be calling elderly services, but do not quit your job or feel you have to be with her 24/7. You don't. Another way to get help is through the hospital, as Grandma mentioned. If she has to go there for any reason make sure the staff are aware that it would be unsafe to discharge her, they can also help find placement in a facility.

The options I see here are..
You and the family move in with mom
or
Mom moves in with your family.
Neither ideal.
Are there any other family members that can help out?
With a diagnosis of dementia your mom should not be alone at any time.
Is there an adult Day care that she might go to while you are at work?
Contact your local Agency on Aging and see if she qualifies for any services.
YOU should not be paying for her caregivers or for any of her other expenses.
Spend moms money in providing the caregivers that she needs.
Consider an application for Medicaid if she needs it.
At some point she will need and qualify for Long Term Care.

Not to jump the gun BUT if she does fall and is taken to the hospital you must tell them that it is unsafe to discharge her to home as she does not have caregivers that are there full time. A stint in rehab will give you more time to find the next step. But it is a good idea to have a Care Plan with options A, B, and C in mind.

Caregiving really does affect the whole family. Sorry for the added stress of the sandwich generation (caring for an elderly parent while still raising your own children). I only see a few options, move mom in with you, have family members take turns staying with her, pay someone privately who doesn't mind a lower wage for multiple hours, or consider a nursing home that accepts Medicaid.