I've used diapers.com and its about the same price as the stores. It was a good experience - fun to get a big old box of diapers on your doorstep without having to lug them around.
I can TOTALLY relate to the shopping troubles. My children are 1 and almost three. I cant believe that so few stores have carts that will accomodate two small children. My regular grocery store has the ratty old ones that look like cars, but they are giant and hard to push, the belts are all broken, and invariably one or both of my children end up hanging out the side or running around the store.
Target - ditto. Too hard to push and the kids dont stay buckled in.
Stores with good carts - Sam's Club has a big, regular cart which will accomodate two kids. We get most diapers and wipes here instead of online (or at babys r us - where we have a card and get a free box after buying 10).
Whole Food and Central Market - Great Carts! The kids sit up high next too you - its like a regular cart, except it looks like a car, and has steering wheels. Good times, if you are a toddler...