You are sadly mistaken on the amount that it costs you do a European vacation. Granted with a full family it would cost more than normal, but it is not even the gross annual income of a person earning minimum wage. I spent this entire past summer in Europe, primarily in Germany with trips to other surrounding countries. I stayed for a little over 3 months, participated in a study abroad program which cost 2500 USD itself and still managed to spend less than 7000 dollars. That included a lot of German beer nearly everyday.

For a month or less stay your largest expense would be plane tickets and with a family of four that could cost as much as 4400 dollars or so in the middle of the summer. Going in May or late August allows you to still see fair weather and have an enjoyable time at a far ticket prices. To spend an equal amount to your gross annual income you would have to be an extravagant spender and have no concept of following a budget.