How can I get a state number to be caregiver for mother & receive payments to do so?

If Mom qualifies for Medicaid and has a need for in-home care they will officially pay for certain hours per day in-home care. Each state varies but when I checked on it for my mom her state was paying $15 per hour, and relatives qualified.
That was 3 years ago so likely be more.

Here is a link to the Iowa Medicaid Waiver program.

https://dhs.iowa.gov/ime/members/medicaid-a-to-z/hcbs/waivers

Parents generally pay from their retirement money for assistance. You might get a few hours paid by the state if your mother qualifies for Medicaid, but it wil be very low pay.