I have a pretty big nappy bag (new for DS2's arrival) from Big W. But even then it is not big enough for the cloth nappies for 2 as well. So I have a separate large wet dry zippered bag (with two pouches). One pouch has wipes, change mat, cream and clean nappies. The other pouch of the the wet nappies. This gets tossed on top of the nappy bag precariously to be carried to the car and then goes in the bottom of the stroller.

Hope that makes sense.