You could try using the pay with points instead of trying to do an award ticket. If you got all of those AMEX cards AND got the maximum bonus points AND they posted in time, you would have 250k points to spend. If it wasn't already set up properly, you can call and have the accounts all combined into one MR account (use the platinum as the main) so it's one pool of points instead of 3 separate smaller pools of points.

If you then book using the platinum card and pay with points, there is a 20% rebate on the points. 250k points would cover $2,500 in air fare and then you would get 50k points back several weeks later.

You don't get as good of a redemption value for your points as you would with miles, but it gives you a heck of a lot more flexibility. You can book on any airline and there will be plenty of seat availability so all 3 of you sit together. Another bonus is that all of you will earn miles on the trip. Make sure you make a FF account for your son too. If his ticket is paid for, he can earn the miles no matter how old he is. If you travel like this each year, you'll build up miles fast.