Hooking up second router/modem?

So I had FiOS in my house for several years now, and we had the router in the dining room, where my computer is and is about the centre of the house. However, I couple of months ago my mum started working from home, and "needed" the router in her new office, which is a floor up and a room over from where it used to be, so now I don't get all that great internet on my computer, my xbox is in my basement, and gets even worse signal. And when i try to Facetime/Skype my brother, who lives far away, it constantly cuts out on my iPhone. So i asked my mum to buy me another router/modem thing to hook up and boost our signal. Unfortunately, hooking it up was not as simple as i thought. Both of the routers were purchased from verizon and run the same actiontech firmware. The coax cable from when the router was in my dining room is still there and usable. Is there any way to use the second router to make the signal in the house much better? Please NOTE: A wired bridge is not possible, and although i'm pretty decent when it comes to computers and programs and such, I know NOTHING about routers/modems.

You can have only ONE modem on FiOS/ADSL/Cable.
=
You did not specify the MAKE/MODEL of the existing router/modem.
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You did not explain why a wired bridge is not possible.
- A wired bridge at the existing router/modem would enable installing a Wi-Fi access points/router in the basement, each floor, even outdoors.

Can you bridge them wirelessly? Do the routers even support bridging to start? Can you not just buy a signal booster instead of another router

Wireless Bridge then.
And no you can't have 2 modems, but you have have as many routers as you like.
My network is set up like this

- Wireless
= Wired
Internet===Modem===1st router ---2nd router===Smart TV

My smart tv supports LAN and is wireless ready but it doesn't have Wi-Fi adapater and it costs about $70 to buy one, and since i have 2nd router sitting in my room. I set it up as wireless bridge.