Everyone has such great suggestions. DD is two and if I'm by myself I generally still do what you do, I just put my vertical Azap, cell phone, and car keys into her diaper bag.
I have the Trim II 35 as someone has mentioned already. If you carry a lot, it may be difficult to get into and out of. Also, the sides are suede so if a juice box explodes in there, it ain't going to be pretty. The Massai is even more difficult to get into and out of as the opening is tighter than on the Trim.
I adore the GPT, but with two children, can't imagine anything without a shoulder strap.
Another bag to consider is the Caravane Horizontal. It has pockets on the outside, has a zip center I believe, and also has a detachable shoulder strap. It's a bit more masculine looking, but highly functional. Here's a pic; it comes in multiple sizes.
http://forum.purseblog.com/attachment.php?attachmentid=79329&d=1160281828
There is also the new Victoria; it looks like a Plume on steroids but with handles long enough to go over the shoulder (the Plume's handles are not designed to go over the shoulder due to the wide profile). It's a bit bulky looking but it will hold a lot, will go over the shoulder and has a zip.
Here's a pic of the original Victoria; it does not have a zip, but is deep enough that it would be difficult for a pick pocket to dip into easily. see post #17 at:
http://forum.purseblog.com/hermes-s...ctoria-polochon-herbag-pics-only-99965-2.html
Otherwise, I agree with Rose about the Kelly--especially if you get one in a 35cm Retourne in a hearty leather like Togo or Fjord (may be a wee bit heavy in Fjord). It will hold quite a bit. And to deter spillage, perhaps use a bag insert like the Chameleon. HTH!
ETA: I do think if you want something prettier that the Lindy in a 34cm is highly practical and just use the x-large Chameleon insert in it; it's a fabulous mommy bag and will hold a lot. I love mine, but I generally do not like having DD's items (that have liquid) in my bags for practical reasons.