I went through a similar thought process with my HHA (me, the wife and two young kids).

I decided it was better to keep us all in the HHA but for me to open an Avios account for spending on people not in the HHA or on things not bookable via BAEC (BAEC seems to have airport hotels only, Avios has more choice of cities and also other things like Eurostar tickets not bookable through BAEC). I transfer as many Avios I need to the Avios account when I need to book though that, and for spending on members of the HHA, I first transfer all but one of my points from BAEC to my Avios so that to prevent my Avios being depleted faster than other members of the HHA.

Remember also that every member of the HHA needs to have earnt an avios within the last year to qualify for Reward flight Saver fares. My wife and I meet this easily because of my paid fares and the fact that we both have a BAEC credit card and things like a card for the Shell Driver's club. The kids might struggle to do this if their only flights are Avios redemptions with Mum and Dad. So I make sure that my online spending (ebay, John Lewis etc) is alternated between my Son's and Daughter's accounts.