First of all you need two DSL modems. If having two is fine, that part is easy. If you want one device to handle both, see
Router that supports 2 adsl broadband connections where that exact issue is discussed at length.
Then you need a router to control it all. You want two separate networks, each tied to their own internet connection. Most consumer devices aren't designed for that, you may be able to work something out with routers that have guest networks and such (most consumer routers revolve around one internal network).
My suggestion is to use OpenWrt. It can fulfill your requirements with inexpensive hardware, but it obviously involves flashing third-party firmware. I could suggest a supported router for you if you give some more details of hardware requirements (2.4/5 GHz wi-fi, gigabit ethernet, expected NAT throughput and so on).
OpenWrt comes with a WAN and LAN defined as default, like most consumer routers. However, you have full control of the switch in most devices, and you can split the available Ethernet ports in as many networks as you require. Think of the default WAN and LAN as WAN1 and LAN1 in your case, and they will be for you. WAN port goes to your DSL modem (modem 1, for simplicity). Then, configure a WAN2 interface and add an Ethernet port to it, this Ethernet port goes to modem 2. Add another network LAN2, and configure it the same way LAN1 is configured, but obviously using WAN2 in place of WAN1. Add one Ethernet port to LAN2, and you are left with one free Ethernet port (most devices have 5 ports) which you can configure for either network.
You can of course use dumb switches to add more ports in each network if needed. You can also configure multiple virtual access points, so that you have wi-fi access to both networks.