The Dlink model that you described is, as John put it, a gateway really and not a router. It is designed to work with only one internal LAN network connecting to one external WAN network. It won't be able to route between two network ranges.
There are two ways to do this really. You can use three simple home routers, or gateways. One router would connect to each switch and act as the gateway for each of those switches' networks. Then the two routers would be connected back to a third router, which would be in a third network range, and allow cross-network communication as well as access out to the internet. However, this can get pretty messy and doesn't operate near as efficiently as the second way of doing this, which is just with a proper business-class router that can do multiple LAN segments.