Q:

How to set up MoCA when already using coaxial for router

Problem
Like many, I have a router in my basement that produces wifi for the whole house. In short, I would like ethernet connections upstairs. Bonus points if I can somehow put a wifi box upstairs too since the wifi seems to cut out pretty often up there.
I have done a little research and MoCA seems to be the most promising solution. As I understand it, MoCa works by:

"Injecting" internet into an existing coax network
Allowing any number (<16) of MoCA adapters to work as nodes to then convert back to ethernet

My Coax Worry
After watching several youtube videos and reading several pieces online, I don't see any reference to people who already use coax for the internet. As seen in the photo linked below, my router is hooked directly up to the coax in the wall, which is how it's connected to the internet. Does a MoCA adapter operate in both directions?
What I want to try
Perhaps this is best explained visually.

Here's what I have now
Here's what I think I need to do 

A:

MoCA uses frequencies far above the frequencies used by Cable TV / DOCSIS operators, in order to send home LAN networking signals over the same home coax as your CATV/DOCSIS service.
In general, you'd put a coax splitter in front of your DOCSIS modem, and run a coax cable from the splitter to the MoCA adapter. Then you'd connect an Ethernet cable from a LAN port of your home gateway router, and connect it to the Ethernet port of your MoCA adapter. Then, yes, elsewhere in your house you'd connect another MoCA adapter to a different coax CATV outlet, and connect its Ethernet port to…whatever you want connected to your home Ethernet LAN, like another Wi-Fi AP, or a PC, or whatever.
Let me attempt an ASCII-art diagram:

                                                         +----------------------------------------------------+
                                                         |            Multifunction Home Gateway Box          |
Coax feed from CATV/DOCSIS operator -- Coax Splitter --- | Coax (DOCSIS WAN) port           Ethernet LAN port | --+
                                            |            +----------------------------------------------------+   |
                                            |                                                                     |
                                            |    +-------------------------------------+                          |
                                            |    |                MoCA adapter         |                          |
                                            +--- | Coax (MoCA) port      Ethernet port | -------------------------+
                                                 +-------------------------------------+

Also note that when using MoCA you should always put a "MoCA filter" (they're cheap small passive devices) on the coax line coming into your house, before it hits the first coax splitter in your home. This not only keeps your MoCA signals from getting out to your neighbors' houses, it also helps reflect your MoCA signals back into your home coax, which helps keep the MoCA signals strong even when they have to traverse multiple splitters.
Also note that there really is no substitute for installing real Ethernet cables in your walls. Trying to use coax or powerline or wireless in the place of a proper Ethernet cable is never nearly as fast and reliable as real Ethernet.

