Although most laptop bags probably would not work this way, I discovered my trusty laptop backpack is an ideal diaper bag. I have a Trager Transcontinental Laptop Brief, which i found at ebags.com.
This bag "conversion" has saved me the trouble and expense of finding a new diaper bag--it has tons of pockets and compartments to keep me organized, and nice thick padded straps. perfect for carrying baby needs and my own books/papers. When I'm not carrying my computer, the internal compartment for the laptop is the ideal size for a happy tushies wet bag. I just had to add an insulated bag for carrying bottles of EBM.
This is not an inexpensive bag, but there are other similar versions of the backpack which probably would work well. I was also glad to get extra mileage out of a bag that has already been a workhorse. As a grad student, this bag has carried all the books and notebooks I need. I also found it perfect for air travel when you want to bring a laptop and a lot of other carry-on stuff, given the new airline limitations.