You have a ton of options to get points. With flying six people total, the points start to deteriate quickly. 

An easy way to earn 100k American Airlines miles is to sign up for the Citi AA card and the Barclays AA card. The Citi card is currently offering 40k points and the Barclay card is offering 60k points. The signup bonuses earlier in the year were much higher. If each you and your wife signed up for each card, you'd have 200k AA points to spend. This likely wouldn't get your18 flights, but it could at least fly you and your family RT to Hawaii. Also, cancel each card after 11 months and repeat this same process in 24 months to get another 200k AA points. 

Where are you flying to and from?