Obstacles - I Don't Have the Time!
How much time do you really need? The time issue is multi-faceted because it isn't just about the actual number of days you spend on vacation. Assuming that your family has one or two members who go to work every day then each day you're in Europe is a day you're away from 'regular' life (and thus a day away from work). The balance needs to be made between how many days you can afford away from work against how many days you can afford to pay for accommodation/food/etc.
You can go for as long or as short of a trip as you like, but when children are involved and you want to maximize your experience (by being awake during your vacation) then I wouldn't recommend less than two weeks. However, if you only have 11 days and want to give it a go by all means do it! Our first trip (when the kids were 3 and 5) was 14 days long and it was great, but we certainly wished we could've stayed a bit longer. It was a nice amount of time for our first trip overseas with the kids and we came home wanting more. (Better to come home wishing you could stay then be plodding through your trip wistfully dreaming of your own bed!)
We've done 2 weeks, 2.5 weeks, and 3 weeks, and all of them are great. If we could go for a month or 6 weeks that would be phenomenal and one day I hope to make that a reality, but for now we'll take what we can get. Budget, school schedules, and time allowances from work will dictate the length of your trip unless you happen to be independently wealthy homeschoolers!