There is an airport hotel where you could book a single room for 5-6 hrs, which also gives 1 hour access to its lounge area for a quick bite.
I do not know if things have changed now but the paid travellers are not given first preference in lounges if its busy. The time your family member transiting is the busiest time in AUH, so better go with the hotel as the price for 5 hrs in the hotel is almost same as the lounge access.
Flights to BLR could be Terminal 1 or 3, and its quite a walk. by the time your family member lands, the gate details won't be available for the BLR flight, so you couldn't choose the lounge accordingly also.
I been in the same situation several times, and everytime I wished that I booked the hotel in advance.