I carry a big diaper bag (the Land's End one I keep raving about) and a little purse. My purse is just big enough for my wallet, a pocket calendar/notebook, lip balm, sunglasses, cell phone and keys. If I need to take my diaper bag into a store or something, I put the purse inside it. Otherwise, I just carry the purse and leave the bag in the car.
I only have one in diapers right now, but I've had 2 in diapers for a long time--nearly a year with ds1 and dd, and again nearly a year with dd and ds2. The LE bag is plenty big for diapers and everything necessary for a toddler and a newborn, plus when ds2 was tiny, I carried all the newborn stuff for him, toddler diapers for dd, and toys and a sippy cup for ds1! Plenty of room.
It is a big bag.....we have a stroller (not huge, but a step up from an umbrella) with a basket underneath, and the bag will fit in the basket, but it takes up all the room. The bag isn't ginormous (I don't feel like I'm carrying luggage, lol!) but it is big enough that I don't want to carry it in and out of stores, etc. It does come with a satellite bag inside, and if I think I'll need to change diapers while I'm inside somewhere, I'll just take the satellite bag and my purse with me instead of the whole thing.
I would NOT want to have 2 diaper bags to tote around and keep up with, but I did make each of the kids a tote bag--just a simple, lined drawstring bag with an exterior pocket--to carry on longer trips. I call them their library bags. They use them when we go to the library. But we also use them when we go to the grandparents--they are big enough to hold a small pillow and blanket, a few books and small toys, a sippy cup, etc. Very simple to make with a yard of fabric (1/2 yard main fabric and 1/2 yard contrast for the lining) and some cording.