I have 2 toddlers (1.5yr and just turned 3). The traditional diaper bag was/is handy sometimes, but I think the bag itself took up more space than the contents I needed. And I was never good at moving my wallet back and forth so I always had my purse too anyways. Now I almost never use the diaper bag. SO, here's what I figured out that works for me:
I keep a small kit/caddy bag in the car with ~10 diapers/Kirkland (large) wipes pack/extra undies/extra clothes/plastic bags, and the small porta potty and a beach towel (for diaper changes on/shade/use as a blanket/clean up spills/etc.). Then keep 1 or 2 diapers (folded and sealed in a zippy sandwich bag) in your purse with the travel size baby wipes. If you are out running errands, you won't need to carry an entire diaper bag everywhere you go, but this keeps the essentials handy and you can go back out to the car in case of an emergency while shopping. I have a medium size purse and can also fit 2 sippy cups and snacks in it if I need to run errands around snack time.
I also use a multi-purpose/beach type bag and love it. It doesn't close up on top, but that makes it easy to throw jackets, snacks, baby dolls, wallet, and diaper kit in and out easily. And I can hang the handles on my stroller clips/hooks or stuff it under the stroller. I use this for things like going to someone's house or using kid's club at my gym. My diaper kit is a gallon size zippy bag with a waterproof pad [cut a crib size pad in 1/4's], 2-3 diapers in sandwich size zippy's, and a small wipes pack.
*When you are out and about having the zip top bag for a stinky diaper is so convenient! The zippy bags also make it easy to see what you are looking for and easy to grab out of the bag.
Snacks go in sandwich-size zippy bags to fit easily in my purse so I don't need a bigger bag. (Sometimes I use the little plastic bowls/cups with lids, but they don't fit in my purse as well AND the kids make less mess sticking their fingers in the baggy than the bowls.)
For amusement parks, parks, or restaurants, I use a regular insulated lunch bag (for milk sippy cups/fruit/string cheese snacks/...) and sling it over my shoulder with my purse.
*sorry if this looks complicated, but it really is easier than all these words make it look :-o