Client and agency. What are the options?

One more question would be if the *family* signed an agreement with the agency about privately hiring a former employees during an immediate timeframe specified in the document (like within a year of them leaving the agency).

I can see how an agency-employed caregiver would feel that the agency is "worthless" but it provides specific benefits to families beyond just caregiving, such as training, vetting, payroll/employment law/tax compliance, subs, liability insurance and legal accountability. The family mentioned in the post can certainly privately hire the same caregiver (if there was no contract) and pay less for care but they won't get any of the other benefits and protections. You get what you pay for in most cases.

Where's your problem then?
This caregiver has already proven that she's good to your family because you want her back. If she's working privately now she can take work with anyone she wants.
I went private duty a long time ago because I saw no reason to continue letting a useless agency who offered me nothing as an employee to rob and steal my hard-earned wages every day. A care agency takes 50% or more of the hourly wage collected for a caregiver. So I went private too for a long time.
Hire back the good caregiver who worked for your family and pay her asking price.
Most of the time insurance will not pay for caregivers unless a do-nothing, useless agency is involved. Is this the problem? You don't want to pay for the care?
If such is the case you'll have to use an agency.

I would think you would be able to work for another client no matter who recommended you and no matter where you met them once you resign from your agency. But if you plan to stay with that agency you may need to reread your contract and I think I would pay for an hour of attorney time to pass this question past legal eagle eyes. You don't want to run into legal problems, not because you will not win in court, but because no one can honestly afford to GO to court. See a lawyer and be certain. You will earn more money by not using the agency. But there are benefits to being backed up by an agency as well, responsibilities they take on for you. Do see an attorney when any question arises that can have legal repercussions.

I wish people would not write in 3rd party. For me its confusing.

From what I read and comprehended, since the new client was never signed up with the agency, then you have no problem. Its when the client contracted with an agency and then wants to hire the caregiver assigned to them privately that the problem may arise. And that problem would be between the caregiver and the agency's contract with the CG. Being related has nothing to do with it.

Non compete clauses are not enforceable in Oklahoma, so that is not an issue. The contract between POA and agency was terminated upon death. There should be no problem, give to weeks and done. If you are trying to do private duty, and if you and trying to receive a 1099, you need to set up a business and less than 75% of your income needs to be from the new client. If not, you need to become an employee of the new client.

It doesn't matter that the prospective client was never a client of the agency. What would matter is if the now-resigned caregiver signed any paperwork when first hired by the agency. They need to break it out and read it to know what they can and cannot do and when. If they didn't sign any no-compete contract or such, then I don't see any problem with wherever that caregiver wishes to work.