Enter the Tactical Diaper Bag.
Think about it, dad's need a MOLLE-based tactical bag for many of the same reasons the military does.
Fast access to mission critical items:
You'd never throw spare mags into your gear bag and hope that you can find them quickly when you need them. Why would you do it for your spare diaper? When you're trying to change a squirming toddler with a fully loaded dirty diaper in a crowded public restroom, you need that fresh diaper ready and at hand! This is the ultimate speed reload...
When I take the kid out for the day, we can be gone for hours, and anyone with young children knows you have to pack for all contingencies: food, more food, extra clothes, distraction devices... I usually skip the stroller and rely only on what I'm carrying on my back, so comfort is absolutely as critical as it would be for any long hike.
Low profile mobility:
If you've ever tried to chase a toddler through a playground tunnel meant for human beings less than half your size, you know why you need a stable, balanced pack that will let you maneuver through tight spaces.
Mission configurable:
This is where a MOLLE system comes into it's own. What you carry depends on the situation and the need. Normal diaper bags give you storage and arrangement options, but you have to fit your personal needs around their design. By contrast, and by its very definition, MOLLE gear configures around your specific need. Plus, when the need changes, so can your gear. Newborns have different needs than toddlers. What if you have one of both? What if you have twins?
Here's my solution to all of the above, using an Eagle Becker Patrol Pack as a base (see the post for a general description of the pack, and then see the Tactical Diaper Bag applications below).
Ziploc bags fold up and then thread nicely into the webbing for quick access.
The front pouch (Tactical Tailor 1H pouch) is accessible without opening the main pack and carries things like sunscreen and the kid's sunglasses.
You can clip anything onto PALS webbing, in this case some web dominators, a few Grimlocs, and a couple spare hair clips in purple and orange.
A Tactical Tailor Strobe/Compass pouch holds a travel pack of tissues readily available for sudden snot emergencies.
The 50 Series Hardcase to the right holds the digital camera ready for Kodak moments.
On the other side I keep a Tactical Tailor 7.62 Single Mag pouch (left) and a TAG Gear folding dump pouch (right).
The open-top single mag pouch is perfect for stuffing bits of trash or odds and ends. While the dump pouch often holds dirty diapers when there's no garbage handy.
There's a zippered accessory pouch in the main flap of the pack good for miscellaneous items.
A Tactical Tailor Canteen Pouch...
...is perfect for holding the most critical items in my book: a fresh diaper and a box of wipes. I throw blue medical chux in for good measure.
...holds an eight ounce bottle of milk so perfectly you'd think it was made for it.