eMTA

I upgraded from a TWC ARRIS TG1672G modem/router to a Netgear CM600 modem and a Nighthawk R7000 router.  The CM600 does not have an eMTA (embedded multimedia terminal adapter) (for internet phone service) within it - the TWC modem does. TWC allows me to retain the TG1672G modem/router (no fees) configured fo handle internet phone service only - this is part of their policy stated online.  My cable into the house goes into a splitter.  One path to the TWC modem, the other to my CM600 modem.  TWC carries its phone service over the cable.  To get the phone service to my house phones, I plug the base phone unit plug into the TWC modem.  My CM600 is connected to the internet coax from the splitter.  The CM6000 is also connected (ethernet connector) to the nighthawk R7000 which in turn is connected to my computer tower (ethernet connection). Here is my question: the TWC modem also neds to connect to the R7000 router (to complete the internet phone service, VOIP) - how do I make that connection?  There is only one ethernet (internet) Cat 5/6 input on the router.  There are four "outputs".  Do these "outputs" serve as either/or input/output much like a USB port.  There is a USB 2.0 on both the TWC modem and my R7000 router.  Will one of the four ethernet connections or the USB 2.0 port work to connect the TWC modem to the R7000 router? . . . Thanks, Rob