How can my sister be compensated as a caregiver through our father's Kaiser benefits?

Vast majority of grown children do not get paid for caring of a parent.... unless the parent can paid they directly from their own retirement fund. If yes, then the sister need to have drawn up an Employment Agreement stating the number of hours worked, the hourly rate, her duties, what days she would have off [if any], and who would fill in for her in case she is unable to help. This Agreement comes in handy in case later down the road your Dad needs to apply for Medicaid.

Normally health insurance and Medicare will only pay for professional licensed physical therapist to come to the house, and nurses who are scheduled to check on the parent.