Not sure if this is what you would consider a "small" bag, but I recently purchased two bags from Massaccesi that don't seem huge, but can actually hold a lot of stuff. The leather on both bags is soft and beautiful to touch and look at, as is the impeccable craftsmanship and design.
One of them is a Little Athena in Port Merinos leather (I didn't have a water bottle, but I did a "what's in my bag" type of post
in another thread) and the other is a Zhoe in Ginger Cuoio Toscano leather (
different thread, but I also did a "what's in my bag" post that did include a 20oz water bottle). The problem with water bottles is they take up a lot of room and they're heavy. I found that I had to juggle/Tetris around some of my stuff in order to hold the water bottle comfortably in both bags. That said, though - I know they can get the job done if I do need a water bottle for the day, and both bags are super comfortable as day bags for outings and such.
I don't have mod shots in the specific posts I linked, so I included both here as attachments.
Keep in mind that I'm a pretty small person (I'm 5'2", and have a petite but athletic frame), so even though I wouldn't consider either of these bags "large", they do look larger on me than they actually are.
I do have smaller day bags (mini to small size like Celine Nano Belt, LV Croisette,
Polene Numero Un Mini) but I can only use them occasionally, typically when I know I won't be out for the whole day and/or I know having a water bottle isn't super important. The rest of the time - as long as it's not a run-down tote bag I think having a slightly larger bag is fine, especially if you find that your needs / daily usage maxes out the capacity of a small bag.
I would also say that while right now it seems like your lifestyle doesn't suit smaller bags, that doesn't necessarily mean it will stay that way forever.

You might find that in the future, once your kids don't need you to hold their stuff anymore, you'll be able to use your small bags comfortably.