What form do I fill out and where does it exist for hiring a family member to fully take care of me?

This is a Medicaid thing and not all States pay family members. You need to call your Social Service Office and talk to a Medicaid caseworker to see if your State has this type of program.

My mother is on Medicare. We had to have an attorney draw up a PCA agreement signed by mom and the family caregivers and notarized. It outlines all of the legal obligations and states that the caregiver has to be paid minimum wage.
The payment comes out of MOM’S money. If you are on Medicaid it will depend on your state laws.

Are you talking about hiring a family member that gets paid by the county or state? This is usually only possible when a person is on Medicaid and it is part of a Waiver program. Each state is different so you'd need to search this on their home state's Dept of Health website under Medicaid and then Elder Care Waivers (or something close to that).

I suggest that you have a Caregiver Contract done.
You might want to contact an Elder Care Attorney. Several reasons for this.
1. Make sure that you have all the paperwork done that you need. If you are needing care now you want to make sure that you have POA set up, Living Will, any Trusts that need to be set up, a Will and End of Life decisions.
2. With the Caregiver Contract it should indicate what the person that is caring for you is to do if they can no longer safely care for you.
3. What can this person do, what can't they do and more importantly what will they not do. (some people draw the line at incontinence, others have no problem with that aspect of care)

These are just a few things to consider I am sure that others will more ideas.