The family member does have UM coverage in this situation. As you noted, a family member is an insured, and an insured is entitled to UM coverage due to bodily injury caused by an accident arising out of the use or ownership of an uninsured motor vehicle. There is an exclusion that applies to bodily injury to an insured who is struck by any motor vehicle owned by that insured which is not insured for UM coverage under the auto policy. And, there is another exclusion that applies to BI to any family member who is struck by any motor vehicle owned by the named insured which is insured for UM coverage under any other policy. But, under the loss as you described it, the auto policy would provide uninsured motorists coverage for the family member.