Another thing you might want to consider is sucking it up and buying the airline tickets on whoever is cheapest. Instead of trying to collect 300-400,000 miles in a short time try and get enough hotel points to stay for free. Hotels in Europe can be very, very expensive and you will probably need two rooms because of the three kids and their ages. You could find that the hotels will cost 300-400 A NIGHT!

Get the Hilton AMX and with your personal and business spending you could rack up enough points for probably 2 rooms for two weeks free. That's a lot of savings especially if you go to expensive cities.

Just another option. I wouldn't want you to try for miles only to be surprised when the hotels cost as much as the airline tickets.