Ok, so my Internet is provided by Verizon. They have to have the router close to the main Television box so that it can be provided with the service. For simplicity's sake, lets call this Room 1. Along with those in Room 1, is a Apple router, called the cloud or something like that. It has a few TB of "cloud" storage and it is what we use as our wireless router, rather than the one provided by Verizon. So, the router provided by Verizon is connected to the wall, which is then connected to both the TV and our "cloud" router which broadcasts the wireless signal.
Now, there is also a wired internet wall jack right next to the Verizon router, which has been connected to it. This jack goes to Room 2, where my sister uses it to connect to the internet, by wire, to her computer. My issue here is that in this room, all of the wires come out for the jacks in the rest of the house, specifically, mine, which we will call Room 3. I have tried to connect another router to the jack coming from the Verizon router, and then connect my jack to that so that I could have a "hot" jack in my room that I could connect my computer to. This, for whatever reason, didn't work. It is possible that the router I used is old and somehow broken.
My question is, is there any way to route the wires in a way that I can have a "hot" jack in my room (Room 3), without depriving my sister of her wired connection(Room 2), like maybe some sort of wire splicer that turns one connection into two? Moving the routers is not an option because of the moronic way Verizon provides their service. Any help is appreciated.