The Respite CARE Act amends the Older Americans Act to establish a federal grant program supporting integrated caregiver services for family caregivers. Eligible organizations, including state and local agencies, nonprofits, area agencies on aging, colleges, and tribal organizations, can receive grants to develop or expand respite care programs that provide temporary care relief to family members caring for older adults, people with Alzheimer's disease, or individuals with disabilities. The bill requires that these services be accessible through multiple methods, including assistive technology, translation services, and alternative formats like American Sign Language. Grant recipients can provide services directly or through contracts with healthcare or childcare providers. The legislation does not specify funding amounts or implementation timelines in the bill text provided.