I am going to cover the answer to your questions but not necessarily in the order you asked them. The reason why you have got 2 coax cables is so you can use one for something like the internet and the other one for a digital tv box. It is possible to use both for internet but not it the way you want to. You can have 2 separate internet connections through VM in the same premises but they would be 2 subscriptions with two modems (shubs). The coax is there for a modem connection and not router so you can't connect another router to a coax cable and expect it to do anything.
Now, to address your dilemma you have two options. You can go down the powerline route which is what a lot of people do but I'll warn you now, it is very hit and miss. For all the people who think they work brilliantly there are an equal number for whom they are abysmal. Taking the Wi-Fi problems out of the equation for the moment, powerline networking is only as good as the wiring in your house which in itself is prone to interference which will degrade your connection and speed. I would only use them as a last resort.
What I suggest you do is what I did a few years ago and is the best thing to do in terms of solid networking, performance and reliability. I have got TV's, bluray players, Sky boxes, NAS' etc dotted all around the house and I wanted each device to have a wired network connection so I knew there wouldn't be any issues if I wanted to stream content from a NAS or youtube over the internet. I ran a patch cable under the carpet from the room where my main router is atm to a bedroom where some of the devices are. Attached to that cable is what you can think of as a main switch (distribution layer switch) and connected to that switch are two access layer switches; one immediately next to it for the devices in that room and the other switch is downstairs in the living room. I paid an electrician £50 to drill a hole through the bedroom wall (Sky cable was coming in as well anyway so it was no bigy) and run a patch cable down the outside of the house and into the living room where the second switch is. There are other routers and switches dotted around serving as wireless access points and stuff but I wanted to explain what you could do.
I would leave your shub where you need it for wireless and if poss run a cable to the other area you need it (you can get flat patch cables to put under carpet) and either put another wireless router there or preferably a switch if all the devices (tv, xbox etc) are static and close enough together that you can connect them all using 1m or 2m cables bundled together to make them nice and tidy. If you go the switch route everything will just work straight away. If you want everything to be wireless then the router will need a bit of configuring for the ip address and ssid etc but we can sort that out if and when you get it all set up.
Like I said though, if you are looking for performance and speed be very weary about powerline networking. I have attached a diagram below just to give you an idea of things have been setup. You can't see where the room are in the house but by taking the time to run two or three cables around the house it is well worth it. The way I look it is from a cost/benefit point of view. Yes it is a pain in the ass to faff around with cabling but once it is done it is done and it will last your many years to come. Networked devices aren't going to go away and if anything, new TV's, games consoles etc are going to rely on an internet connection even more in the future so you had might as well start as you mean to go on and do the job right first time round. That way when something doesn't work you don't have to sit there trying to work out whether the connection issue is with the device, it is a wifi issue or powerline issue (and trust me, may people have joined this forum for exactly this reason and it is very laborious troubleshooting it and trying to work out where the issue is).