Are you considering the damier line at all? I don't have children, but if I did I think I'd be worried about the untreated vachetta leather of the mono line. The damier (not Azur) line would be more forgiving of sticky fingers and juice stains.
Also, you might want to think carefully about any bag that has the vachetta leather bottom as I've been reading here on the forum that many people are unhappy with the way it get really marked up so fast. I would go for the Batignolles horizontal myself--I've heard the the vertical version is a black hole that you are forever rummaging around in to find your wallet. Plus the BH does fit over the shoulder as well.
Lastly, may I suggest you visit the LV shop at the Wynn. I spent a couple of hours there last July picking out a bag and it was such a pleasant experience. My SA there, Edward is a lovely gentleman with 20 plus years experience in the leather-goods business (like me) and treated me like a queen despite the fact I only had $500 to spend. And when they didn't have the exact bag I wanted he called LV Caesar's and arranged a taxi for me to run over and buy it from there. And this after he showed my like ten different combinations that added up to my $500. What a gem!!!
Sorry for the long post.