Mom wants to give money to her kids, but sister says she needs it for her care. Should I tell mom that it will be used for her care instead?

Very, very few people say they WANT to go into a NH.  However if she needs to, giving away this money will likely delay by months when she can do so, if she needs to go in within the next 5 years.

Her best thing is to write a Will leaving her estate to her children to split evenly. Like said, giving the money to her children now would effect her being able to receive Medicaid in the next 5 years.

Your profile mentions Dementia. Your sister has the right idea. Let her sign the checks just don't give them out. Let the sisters thank her. Little white lies sometimes need to be used. I would also write Void on the checks especially the signature. This way they can't be mistakenly used.

I would go to an elder law attorney before you do anything, for your mother's protection. No one wants to have these conversations but they are imperative when dealing with family, money and memory loss.

Mom is welcome to give away her money as she pleased, but that would be if she KNOWS she has PLENTY of money to pay for say memory care for 5 years. What we WANT and what we have to put up with are two different things. Mom could tomorrow come to need care that cannot be provided in her home or by her family. She could quickly go through her money and need government assistance. She would then be faced with the Medicaid Lookback which you can easily look up. You mention that Mom is getting forgetful. So I must ask, who is her POA if her financials need looking after. Has she appointed a family member or a Fiduciary?
So again, it depends on your Mom's financials. If she has upward of one million she is somewhat self insured, and could survive with no governmental help for 5 years. Then she can give some money away. Many seniors do, and help children with down payments, with college for grandchildren. But in these times they are the more lucky, more rare among us.

mom's money needs to pay for her care - she doesn't have a choice about nursing home, don't let her hold everyone hostage for an inheritance.