I don't believe there is a way to hook up two modems to the wiring and have them function independently. You might be able to use one in a "repeater" mode, though, and that could possibly be done wirelessly. There are also specific repeater devices you can get to extend the signal, and that might be easier to do. I suggest you contact the manufacturer of your modem to ask what is possible with that specific model, and whether they sell a repeater device that would be easier to set up than a second router.

By the way, have you confirmed that the streaming does not work well, or is that just a statement in the manual?

By the way, I have a similar situation. I have a DSL modem with a 3MB signal that is connected to a router in an upstairs closet; my tv system is in the living room downstairs. I have an older DVD player without a streaming capability, but wanted to be able to stream Netflix movies. I bought the Roku wireless device that Netflix sells, plugged it in to the back of my tv as an additional input, and set up the connection in about 2 minutes. I am able to get maximum quality every time I use it unless someone else is using a computer in another part of the house, in which case picture quality drops down a little.