I dont have 2 kids but instead of spending heaps on a "nappy bag" we just bought a slazenger sports bag for $20 (reduced from $40 ). It's huge and fits plenty in, the only problem is because there's so much room I put in more stuff than we need
RE your DS's bag: you could just let him take it with a couple of things in it and if he doesn't want to carry it, it'd probably fit inside the other bag. Or use it as a lunch bag?