switch – Connecting three rooms with one router

I have a router that has 1 input (for the Internet connection) and exactly one output for LAN. Recently, I’ve moved to a house that has 3 different rooms and one management box in the wall of the hall and I wanted to connect all rooms together, behind the router.

I have a switch inside the box that connects all rooms in a single LAN – there is also a modem device that converts the fiber signal to RJ-45. Unfortunately, there is no place for my router in the box… But I also wanted to put it inside the middle room for maximum Wi-Fi range, so I hoped it is for the best. I thought I’d have to something like this:

Room A --
        |
Room B --  SWITCH IN THE BOX | -- Room B -- | Router | MODEM IN THE BOX
        |
Room C --

In other words, I hoped that the middle room has 2 RJ-45 sockets. One socket would be taken for sending the modem’s Internet, the other one would go back to the switch in the box (probably using another switch there, too), which then would connect other rooms. It would look like this:

  Modem from the box -> RJ-45 no. 1 -> Router -> Switch in the room -> Other devices from the room
                                                                    -> RJ-45 no. 2, which goes to the main switch from the box -> Other rooms and their devices
  

Unfortunately, each room has only one RJ-45 socket, which made it impossible for me, because the Internet and the LAN would have to be sent over the same cable. Either I would have LAN devices as siblings to the router, or I would have conflicts/loops in the network.

What options do I have now? I recognized the following choices:

  1. Invest in a patchcord splitter in both ends of the cable (which would convert 1-node socket to 2-nodes). This option would halve the performance of the connection, as far as I can understand, which isn’t the brightest idea for the main router? The cables are cat. 5e.
  2. Try to find a “smart” device, something like a switch, which would have multiple ports and would know that the first one is the router – and made the other ones behind it? I’m afraid that this option is either very expensive or impossible to do.
  3. Hire a specialist that would make a new connection in the walls for the router – very expensive for me, as the walls are already finished (painted etc.)

Is there any other option I am missing? Would the first option severely slow my connection?