Weddings are about family. Family includes all generations--From great-great-grandparents to great-great-grandchildren. They all should be welcome. I've never been to a wedding that didn't allow them, and I've never seen a child interupt or do something significantly inappropriate at one. (Some things have happened, but they fall more in the category of "cute/humorous" than "disruptive".)
I don't buy that you're concerned about the cost involved with inviting the kids. If you were that concerned, you wouldn't have booked a place that charges $175 per person
My wife and I were married fall of 2005, and I don't remember any wedding reception facility anywhere in our area charging anywhere near that exhorbitant of a fee. If you're willing/able to pay that amount for 100 guests just for the reception hall, then clearly the cost of your wedding isn't a major concern.
Invite the kids. In some way that you can't fathom at this point, they'll likely provide you with the best memories of the event. You claim that it's "your day, and you would like it the way you want it"--I disagree. You don't want it to be the way you want it--you want it to be the way that provides the best long-term memories, regardless of what you *think* you might want now. And I say with full confidence that that involves inviting the kids.
One of the fondest memories of my own wedding is my then-3-year-old niece, who was our flowergirl. During the rehearsal she kept grabbing huge handfuls of flowers and tossing them rapidly--and her basket was empty by the time she got 1/3 of the way down the aisle. So we explained to her that she had to do it more slowly, and save the flowers. So during the actual ceremony, she kept reaching into her basket, pulling out about three petals at a time, dropping them lightly, then she'd take a few steps--and decide that she wasn't saving enough petals, turn around, pick up two of the petals she had dropped, and put them back in her basket. She did this the entire way down the aisle, getting laughs the entire way. Is this the type of "disruption" you're trying to avoid? Because it's moments like those that make weddings great.
Just curious--do you and Rachel have any plans to have kids of your own at any time? Because if you are, but you have this negative position about having children at an event as important in your lives as your wedding, I highly suggest reconsidering those plans. If you can't handle having other people's kids, under their parents' supervision, participate in your lives for a few hours, then you're definitely not ready to have your own kids, without outside supervision, participating in your lives 24/7...