What is the proper way to let a caregiver go?

I'd check your contract or paperwork that you signed in the beginning to see if there are specific provisions about it.

Let the agency know of your plans. This way they can plan on reassigning your caregiver when the time comes.
There should be something in the paperwork about notice.
I also suggest that you write 2 letters. (If appropriate and true)
1. To the agency telling them that you valued this Caregiver and that you were pleased with the level of care that Mom received.
2. To the Caregiver telling her/him that you were pleased with the level of care that was given. That Mom will miss her/him.
Caregiveng is an ever changing thing. As people decline a higher level of care is required. The caregiver that you start with is usually not the one that is the last caregiver. This is expected.
Your first priority is to Mom and her needs. It should also be a caregivers priority. They / the agency will easily find another position. There are far to few good caregivers.

Also remember that the caregivers' pay is (in most cases) low, that it's non-existent between patients and when the caregiver is sick or taking care of a sick child (or husband or mother). It's so very appropriate to make sure you meet the required standard of separation pay and the 'usual' (if more than legally required). I suggest, too, to be more generous if you can be.

Please think more about the long term effects on your mom as well as your ability to have a voice in your Mom’s care once you commit to a residential community. Your mom is used to individual care with the total focus on your Mom’s well being and care. This will never happen in any residential facility. Your mom will not be cared for to the degree and manner she has been accustomed. Please check the ratio of true, certified staff for each patient - especially during the night shift. Also note the cost of laundry, the increase in theft of clothes, belongings and other items once the family is no longer able to be in charge of your Mom’s care. We opted for private caregivers that were not affiliated with agencies but had wonderful references from other families. Our experience with in-home caregiving for the past three years was that my mom lived a lot longer and with a better quality of life being in her own home with 2 24/7 caregivers. I would not have wanted mom in a nursing home or SNF based on the care given to the parents of our friends and the lack of care and consistent commitment to quality continually expressed by others who related stories of nursing homes. You have very limited control of your loved one within the restrictions of any residential community. You will lose your compassionate caregivers very quickly as they’ll find other jobs immediately. The money may not be the best consideration when it comes to your mother’s care.

Aside from any contractual obligations, it is nice of you to be concerned. But do bear in mind that, for much sadder reasons, caregivers and their agencies are very used to "losing" clients - and I'd expect their termination clause to take that into account, actually.

I am actually going to put my mom in a private home. Actually a house. She takes in 6 residents. Caregivers work 3 12hr shifts. Picking their days. The house is 15 min, from my home vs. 45. I will still handle my mom, the same. Same docs, hair appt, and outings.

Ihave1now, I agree with Sunny above. Since the caregiver is through an Agency, it should say on the contract how many days notice you would need to give them. You would pay for the days not used.

I would also like to add to this. Is that many a times I have gone to my moms house, only to find her in bed, and wet. Now, I know it's a hard job, and just like a baby, everyone rest when baby sleeps, or finishes needed tasks. But my mom is also alone.......only with caregiver.....no stimulation until I come into town.

The answer will be depend on whether or not you had a caregiver contract.

I am actually going to put my mom in a private home. Actually a house. She takes in 6 residents. Caregivers work 3 12hr shifts. Picking their days. The house is 15 min, from my home vs. 45. I will still handle my mom, the same. Same docs, hair appt, and outings.