We share your frustration, even though there are two of us in our house - we both work very full time.
This year's winter break, we have resorted to hiring a nanny, since our 18 month old ALSO has two weeks off at her daycare, which I think is rediculous. Especially since we still pay the full month's rate. Our almost 5 year old was going a little nutty staying at home with sister and nanny so I just paid another $55 for a day of camp with a friend at the Y. He will also go there all next week if today goes well.
I think sending the kids to grandparents for lengths of time as they get older may be our answer, as friendamy suggested. Also, since I run camps through my work, they eventually will be both attending A LOT of camps. We also occasionally send our son to his old daycare provider for a day here and there when he school closes for any reason.
In general it's a lot of juggling and pre-planning as much as you can. Financially, we set up what we call our "nanny account" (even though we don't typically use nannies), and we both have funds automatically deposited into this account each paycheck. We use this account for childcare, and all extra curricular activities like swim lessons, music classes, etc. It has worked out well so far.
It is impossible to stretch your vacation to cover all of the days off. Not to mention that you might actually want a real vacation at some point. We have decided that we will not be doing any vacations in 2013, since we are heading into our 2nd year of infant care/preschool expenses. Once our son starts Kindergarten would should begin to see some relief. Our school's after care also provides coverage for no school days and breaks as other posters have said. It's the little one we have to figure out!