MoCA 2.5 Adapter Kit with 2.5G Ethernet Port and PoE+ 30W for Ethernet Over Coax – Ideal for Wi-Fi 6E/7 Access Points, IP Cameras, and More – Model KB-M3-03

You might like to use the Kiwee MoCA adapters that have PoE+ Ethernet port so that you don't need a separate PoE injector for your APs and / or Flex Mini switches.

You might like to use the Kiwee MoCA adapters that have PoE+ Ethernet port so that you don't need a separate PoE injector for your APs and / or Flex Mini switches.

Here is a diagram that shows how MoCA works with DOCSIS 3.1 modems. Splitters should be 5-1675mhz and MoCA filters should be 70db. Looks like you can replace that 3 way with a 2 way and add a 2 way in the box per the diagram and have MoCA and TV to all three rooms. So Router / modem in one room on one line and the other 2 going to the additional rooms. I like the Kiwee MoCA adapters that have PoE+ ethernet port.

Since you have the coax, here is a diagram that shows how to use MoCA adapters with DOCSIS 3.1 modems. Be sure to use 5-1675mhz splitters and 70db MoCA filters for best results. GoCoax and Kiwee MoCA adapters sold at Amazon are good choices. The referenced Kiwee model has PoE+ Ethernet port. I use that Kiwee model to connect a Unifi U7 In-Wall AP using the PoE+ and then connect a Flex Mini 2.5 switch that is powered by the PoE port on the AP. My system is all UniFi.