What you could do possibly is buy 3 "cheaper" seats, and set up a tour of Fenway Park for before the game. (Not sure where to look online, one of the other guys set it up) Part of the tour is sitting on the Monster during batting practice after standing on the field behind home plate and having a chance at some autographs. In fact I would suggest the tour regardless of where you sit, it's a pretty amazing ballpark.
I'm not sure how long you'll be in Boston but if you have an extra day and your kids are old enough to appreciate history, I HIGHLY recommend walking the Freedom Trail. It starts in the oldest city park in the United States, and the one of the sites along the way is a cemetery where Paul Revere, Sam Adams and John Hancock are buried.