I bought a binder with paper and keep a log of what we do daily for the daughter of my client. Is that considered my property?

Logically, it would seem that it's yours, though who knows how the law might interpret the situation, if it came down to your being challenged for ownership. If the daughter of your client is saying that it should be hers to keep when you move to another job, why not make a copy of it for her and keep the original for your own records? Just a thought.

I have a notebook on my counter at all times for my caregivers, and family. I think if you write things down for yourself at home, thats one thing. But here, we all write about what we do for mom, her bathroom visits, her moods, her pills, miralax, etc. I consider this private information. My caretakers do not talk to me about their other clients personal info and I expect them to keep what happens at my home confidential also, and they understand that. You can always ask for a reference from this woman on what you do for her Mom, if thats what you need.

I would have to ask why you wouldn't want her to have to help with the next caregiver. But I totally agree with Nanfranp, legally I think it is yours but since it includes information concerning a client, she has a right to see what is in it. So the best solution is just to give her a copy of it.

its yours. That is your record keeping, and you should keep that incase anything comes up in the future. Unless its a pain in the butt, you could give them a copy.

I know that the circumstances are not exactly the same, but when you change doctors & ask your original doctor for your medical records, he/she does not give you the originals. He/she gives you copies & he keeps the originals. This is similar to your situation. I also think you should give copies to your client. Prior to making the copies you may want to black out any personal notes that could cause problems.

Why do you ask?

I know that things I write while I am on my job, for my employer, are my employer's property. If I want to keep a copy when I move on, I ask permission. Sometimes I get it, sometimes I don't. (I am a consultant, and all clients have me sign a confidentiality agreement when I start.)

I don't know if this is similar to your situation or not. You might ask how the client feels about it.

When I worked in a Doc office, here is one scenario:
Patient demands original records created in the office by the Doc, about that patient's care. Patient wanted ALL records, both health and billing, of their ever being in that office, leaving no paper trail they had been there.
--Lawyer advised:
While records DO belong to the patient, by law [in CA], they can take them from the office they were created in, BUT CANNOT demand that no record trail is left, simply because that leaves the Doc open to legal maneuvers, and having no records would mean the Doc had no way to protect themselves from legal action, tax actions, or further contact from the patient.
THEREFORE, it was advised to keep copies of the records.
He further advised that, due to the patient being behaviorally aggressive, to make the copies quietly, so it was less an issue, and just not bring it up, whlie giving the appearance of surrendering the original records.
By law a patient is NOT entitled to take all records from the practitioner.
NOW...
This may be extrapolated to determine for your caregiver records.
One might ask,
---Is the daughter, or anyone else, pressuring you to give over the records you keep?
---Why are you keeping records of client care, too?
---Are you working for a home health care organizaton?
---Why are you keeping records of what you do for the daughter of the patient you caregive for?
---If you work for a home health care organization, does the organization you work for ask you to keep the log describing what you do for the client's daughter? Why?
---Why does the daughter want a copy of that log?
---Is the daughter the client, or, did she hire you directly?
---Did the daughter hire you through an agency?
---Is the agency still in the client-caregiver relationship?
IF you provide care or services for a non-client, during paid work periods for your client, that might be construed as conflicting with caregiving for your client, or, services that might otherwise be disallowed for payment by a home health care organization one might be working for--so they might have had difficulties with this family before, with other caregivers, and need documentation, for instance, to make more detailed rules for caregivers assigned to that family, or perhaps even to have legal grounds to stop providing caregivers to that client.
It is pretty common for family members to assume that a paid caregiver is there to help everyone in the family who is present [like a family maid might be expected to do][& often pressure the worker very strongly to do their bidding].
It is a difficult situation for the caregiver, because it can get them taken off that case, or even fired: the caregiver's employer is not the client, but indeed, the home health care organization.
If the agency is a STATE agency, like through DSHS [welfare], they tend to be more strict as to what activities caregivers perform while on duty as caregivers for specific clients, since the State is paying for services rendered. They tend to consider it fraud if a relative [or friend] has a caregiver do things for them while supposedly caregiving an assigned client: they are getting services for free, essentially.
The situation differs some, if you are an Independent Worker [in which case you need to keep records for your own protection both legal and financial].
As an independent caregiver, you have less support, and are more easily open to legal adverse actions from dissatisfied clients; you lack the weight of an Agency behind you, among other things.
It still boils down to family member getting services for free, since you were only hired to caregive for the main client.
Anything you do for the daughter is therefore a "freebie", you being nice to relatives on your own volition...the more you do that, the more is expected, though.
IF you are independent caregiving, it might be a good idea to let new clients know, up front, that you do keep records of daily activities while on duty there, so there is no confusion later.
It is at that start point that rules, practices and protocols can be given to the hiring agent/person in writing for them to read before agreeing to services, and have them sign that they have read them, and let them keep a copy.
If they decide they want copies of records, you are prepared to create copies for them.
[Some practitioners automatically make records copies and hand them to clients at each appointment].
IF you took initiative to keep that log of activities you do for the daughter of the client, as an independent Caregiver, in the middle of the caregiving of a client, one might wonder what circumstances exist that need records kept that had not been kept before.
It might be seen in a simliar light as records created in a Practitioners office, so one has referrence to what services are rendered, and how best to proceed with care, and to be accountable for tax purposes.
IF you are keeping that record at the request of an employing home health agency, it might be argued that that record belongs to the agency--which means it is still NOT the daughter's.
HOWEVER, if the daughter is concerned that you might be logging in activities that didn't get done, she probably could have copies of the log--AFTER a section is done. More likely, a relative who demands free services for themselves, is worried about losing services for the actual client, or, fears loss of privacy--in which case, are you under some kind of expectation to maintain privacy? (as medical professionals, ministers, etc. have).
Depending on what State you are in, she might even demand and be entitled to the original records, while you keep a copy (see above story).
By one party keeping a copy of the originals, it tends to prevent doctoring records after-the-fact.
They are still records and can still be used in court, one way or another.
Records kept while in the line of duty, pertaining to duty, therefore might be construed as belonging, in part, to both parties.
IF however, you write notes AFTER work hours, on your own time, like creating a "diary", and it is about clients you worked for, it might more appropriately become your property, and less the client's.

It does sound like there is more going on there though...so if more information is share-able, you might get more specific answers.
Hope this helps.