Availability of award space to EU and US is hot property so if you can find 2 business class award seats, you are one of the luckier person. That said, there are instances where you do indeed find more than 2 seats.
If you have sufficient points, you could consider securing 2 of the 3 seats with points for kid and wife. Then possibly redeeming or paying for a fully flex premium econ/economy fare for yourself. Then you would have to keep checking and see whether they release any more award business class fares. Cathay for 1 is pretty good at releasing more award space 14 days prior to departure. Once you find the 3rd seat, you can redeem then cancel the 3rd ticket once the 3rd award ticket has been confirmed.
Alternatively, you could consider flying separately (± 1 day), though that would sound very unattractive. It is a popular option for couples with 2 kids. 1 parent + 1 kid per flight.