My mother has been told by someone that if family members are on her accounts, they will take everything. Only two daughters and we all get along.

Suggest Joint tenant with Right of Survivorship. The elderly person will probably need to be competent to make this the direction on the account. Try to get some neutral party like a lawyer to explain to mom before its too late. Makes things much easier. If not that, file the Durable Power of Attorney with the banks.

I can see from our answers as to there being confusion about what you mean here.
You use the word THEY in referring to these nebulous others who may take her money. What does your mother mean by "they". Is she afraid relatives may steal her money?
Because of course, if they are not on her account as POA, they absolutely MAY. And we have seen that on this forum. One sibling of another gets put on an account and takes ALL THE MONEY. So good on Mom. She scores if that's what she means.

Why do you think the state will “take” everything? This is not communist China! This is the United States of America, for Pete’s sake. Where such ideas come from I cannot fathom.

If she doesn't want you on the account, try to get POA on the account. This allows you to help her but, makes you a legal fiduciary and that is governed by state law and any shenanigans are prosecutable.

Maybe she would be open to that route.

I told my dad that he needed to do something to make it easier for me or I was not gonna help him. Making it as hard as possible for me was a boundary that I would not budge on. If you do that, I'm out. Period.

This issue is one many caregivers deal with. It is absolutely true that anyone on the bank account can take all the funds. It is also true that if mom can not access her accounts for whatever reason, it will be very difficult for you and sis to take care of her when she needs you to if she doesn’t leave legal access through the bank account or a POA. It is a matter of trust.
When my mom had her POA done her attorney told her, you do realize your kids can take everything?! She did. But as far as I know, she never worried about that. Although she kept a close eye on those bank statements. 🤔
And we had no problem with doing what she wanted. But that’s me and my family. It is your family that matters here.
When you say someone has dementia, often the forum members will opine that it is too late for the POA to be assigned. That is not necessarily true. You need to do as Geaton said, take mom when at her best to an attorney you have fully vetted. This needs to be an elder law attorney. The attorney will know whether or not mom can understand what she is doing. What she is signing. Make sure you really want the responsibility and insist that sis also be named as co poa or successive. Often caregivers die before the one being cared for.
There are stages to dementia. Early on in the first stages, people still work, drive and take care of business. You probably already know if mom is able to make these decisions on her own. Don’t wait to get it resolved. We never know when we will need help.

Personally I would not do one thing for her until she got this straight. It is too hard to volunteer your life to caring for someone who doesn’t trust you. That’s just me. Again, you do you.

State will take nothing unless she is made a ward of the state and they spend it for her state assigned guardian and her care. Either way, you now know some of what you will have to deal with going forward. It’s not easy taking on the care of another. Big hugs to you and know that you can learn a great deal on this forum of what others go through. Legal advice from a qualified, elder attorney in your mothers state is very helpful.

If you are not on her bank accounts, you must get POA, because if she ever becomes incapacitated and needs to access her money to pay for care, nobody will be able to do so. In my opinion, it is best and easiest for all involved to be on all of her accounts. I was for my father, and I am on my mother’s accounts. If she suddenly passes, and you are not on the accounts, you will have to go through probate which is a pain.

Maybe the person who told your mother these things had a bad experience in their family.

This person may mean well but how your mom handles her finances is her business.

Can you elaborate on what you mean by saying that the state will take everything?

I am not sure that I am following what you’re saying.

Your profile says that your mom is living at home. Are you referring to the Medicaid stipulations?

Why would "the state take everything"? Is mom in Skilled Nursing care with Medicaid? If so, Medicaid has strict rules about everything and you're better off sitting down with an elder care attorney to get all these financial matters ironed out.

Good luck to you.

Paranoia is a common behavior with dementia. There is not a lot that can be done about it, except maybe wait to talk to her when she seems more like herself. My 95-yr old Mom has pockets of paranoia. I make sure all our important meetings are in the morning so she is not tired or sundowning.

It isn't sounding to me as though you are aware of POA and how to do Power of Attorney for your mother?
And if your mother has dementia then it is too late for her to confer POA upon one of you.
As this would require a lot of legal documents, record keeping and your learning how to issue her checks for her as her POA, I think that you yourselves are not ready to assume financial responsibility for your mother. If you meld your names on her accounts you may come into legal issues such as "gifting" and your mother would not be eligible for any assistance in future from Medicaid should she require it. The waters would be very muddied.

I think that you should consult an elder law attorney.
There you may discuss if you should hire a Fiduciary (the attorneys work with them through the courts where elders without any family at all need the state to take guardianship and manage the elder's assets in a legal manner).

Do not attempt to do financial management of your mother's affairs if you are not absolutely certain of your abilities to know what's required legally in doing this.

You can also talk to APS about your mother's assets and your worries over who might manage and protect them.

Wishing you the best.

Once someone is added as a joint owner, they can withdraw money from the account just like any other owner. I am a joint owner on my mom's account, but since I am too honest for my own good, there is not a problem. However, you can find tons of posts on this forum of family members who become a joint owner on mom's account, and then drain every last cent.

I can't tell you if becoming a joint owner on a bank account is a good idea or not. That will depend on the ethics and greed of everybody involved.

If your mom has been diagnosed with dementia she probably can no longer sign documents of any kind.
If you even suspect that she can no longer handle her affairs you need to see an Elder Care Attorney there is a possibility that you may have to obtain Guardianship.