Ive never really been interested in accumulating points, figureing that I would have to spend a gazillion dollars to earn a few.
Firstly, get interested

and then secondly, start reading alot and realise that you don't need to spend a gazillion dollars to earn a few!!
The first thing that pops into my mind is "you need to start earning using a credit card" and use the card everywhere and anywhere you can! Just make sure you pay the closing balance in full every time it's due, otherwise the points earnt is outweighed by the interest charged.
With a family of 7 I can see a HUGE weekly supermarket bill, and with some of the newer cards, you can earn up to 3 points per $1 spent from the credit card itself. Major supermarkets accepts all types of cards and don't charge surcharges, why pay cash when you can pay with card and earn points
Simple example, let's assume you spend $300 per week just at the supermarket, $100 on petrol, $200 pw on other things like utilities, rates, health insurance, + miscellaneous expenses and you have (for eg.) an American Express Edge Card.
Supermarkets 300 x 3 = 900 points pw
Petrol $100 x 2 = 200 points pw
Miscellaneous $200 x 1 = 200 pw.
In this example, you would earn 1300 points p.w, or 67,600 each year.
Now we're just getting started; you got to look out for promotions where you could earn extra points etc and they all start adding up.
The only negative I can see from your situation is ..... redeeming 7 seats at once. I've never looked/searched at booking 7 seats at once so I don't know how easy it is.