As parent of twins we've always been ignorantly overwhelmed with parenting workload. Of course the brunt of this has come and passed with the advent of potty-trained kids (so thankful for this!!). One item that certainly made a difference for us (for any parent, for that matter) is having a good bag/organizer system. With twins it was even more important (for those with triplets .., godspeed). We automatically skipped the standard diaper bag, especially the expensive designer ones that put more effort into the fashion than the function.
The no-brainer for me back at that time was a standard messenger bag. Big. Waterproof (thinking about all the wet clothes). No zipper to worry about and can be opened up with one hand. Shoulder strap. Etc... And we ended up buying two on sale at REI. One medium and one large. We still use the latter today for overnighters and sleepovers. The brand we bought was Timbuk2. The small one is now my work cummuting bag. (I did recall think when we were shopping for "diaper" bags that if we bought a utilitarian bag like a messenger bag we could use it once the diaper phase had ended. Smart choice. I've also tauted to other friends and paretns the benefits of the messenger bag as the perfect kid bag.
In any case, it put a smile on my face when I saw today the Timbuk2 now sells a diaper-specific messenger bag. They even named it the Stork. If only they had this 5 years ago.