Can a professional caregiver (RN) be paid to provide care to parents if the long term care insurance policy excludes family members?

If the insurance policy does not allow for family members, it doesn't matter if the person is an RN, and LPN, an MD, or a CNA.
Many insurances have a 'no family' policy.

Read the policy to see if there is an exception for RN family members who work through an agency or if the insurance may allow case by case exceptions for those in special circumstances (isolated areas with few caregiving options?).

Not if the professional RN IS a family member, no. She would be excluded.