Are there any programs to help children financially to care for household needs for parents with mild dementia?

Candoll, the vast majority of grown children who are caregivers for their parent do not get paid, unless the parent can pay from their own savings.

Another option is to see if your Mom can apply and be accepted by Medicaid [which is different from Medicare]. Depending on your State, each State has their own rules, regulations and programs.... your State might offer payment to a grown child caregiver, but the pay would be very minimal. The State might have Aides who will come to the house for a few hours each week.

As for your Mom's finances, that would be up to the financial Power of Attorney to take care of Mom's finances. I hope your Mom had appointed someone and had an Attorney draw up the paperwork.

I see where she is in independent living. If there is money, maybe time for Assisted Living. My Aunt lives in an independent living but can use the services of the Assisted living in the same complex. She just pays xtra for them. Call your County Senior Service or Office of Aging. They may have services Mom could use or aim you in the right direction.